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Gauge (non-)invariant Green functions of Dirac fermions coupled to gauge fields

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X i v :c o n d -m a t /0112202v 3 18 A u g 2002Gauge (non-)invariant Green functions of Dirac fermions coupled to gauge ?elds

D.V.Khveshchenko

Department of Physics and Astronomy,University of North Carolina,Chapel Hill,NC 27599

We develop a uni?ed approach to both infrared and ultraviolet asymptotics of the fermion

Green functions in the condensed matter systems that allow for an e?ective description in the

framework of the Quantum Electrodynamics.By applying a path integral representation to the

previously suggested form of the physical electron propagator we demonstrate that in the massless

case this gauge invariant function features a ”stronger-than-a-pole”branch-cut singularity instead

of the conjectured Luttinger-like behavior.The obtained results alert one to the possibility that

construction of physically relevant amplitudes in the e?ective gauge theories might prove more

complex than previously thought.

I.INTRODUCTION In a generic many-body fermion system,a repulsive electron-electron interaction is normally expected to result in a suppression of any amplitude which describes propagation of fermionic quasiparticles.For instance,in the phenomenological Fermi liquid theory,the residue of the electron Green function G (?, p )=Z (?)/(??E ( p )+μ)gets reduced compared to the non-interacting value (Z (?)=1),thus exhibiting a partial (0

Ψ,A ]= d x [

N f =12g 2(?μA ν??νA μ)2](1)

where,for the sake of completeness,we also included a ?nite fermion mass m .

Among the previously discussed examples of the 2D condensed matter systems that support the Dirac-like low-energy excitations and allow for such an e?ective description are the so-called ?ux phase in the planar quantum disordered magnets [3,4]and the layered disordered d -wave superconductors with strong phase ?uctuations proposed as an explanation of the pseudogap [5,6]and insulating (spin density wave)[7]phases of the high-T c cuprates.Also,the non-Lorentz-invariant version of QED 2+1was shown to provide a convenient description of the normal semimetalic state of highly oriented pyrolitic graphite [8,9].

The number of the fermion ?avors N depends on the problem in question,although it is not necessarily equal to the number of di?erent conical Dirac points in the bare electron dispersion of a lattice system.In all of the previously

discussed2D examples[3–9],N=2is a number of the electron spin components,while the number of the conical points turns out to be either two[8,9]or four[4–6])which merely forces one to use the four-component Dirac fermions

and the corresponding(reducible)representation of theγ-matricesγμ=σμ?σ3constructed from the tripletσμof the Pauli matrices.

In the abovementioned condensed matter-related applications,the e?ective gauge?elds serve as a somewhat exotic, yet often more convenient,representation of such bosonic collective excitations as spin or pairing?uctuations,while the Dirac fermions correspond to the auxiliary fermionic excitations such as,e.g.,spinons[3,4],”topological”fermions [5–7],and so forth.Generically,the quantum mechanical amplitudes describing such degrees of freedom turn out to be gauge-dependent,while all the physical observables which experimental probes can only couple to must be manifestly gauge-invariant.

Among such gauge-invariant amplitudes,is the one containing a phase factor(sometimes referred to as a”gauge connector”or a”parallel transporter”)

GΓinv(x,y)=<Ψ(x)e i ΓAμdzμ

(4)

x D+1+η

where the sum is taken over all the Fermi points.

In the present paper,we employ a functional integral technique to compute the function(3)and discern the true nature of its singular behavior(if any).This approach which had been pioneered by Schwinger and later advanced by a number of other authors(see,e.g.,[10,11]and references therein)exploits a functional integral representation of the exact solution of the equation for G|inv(x,y|A)as a functional of an arbitrary con?guration of the gauge?eld A(z).Subsequently,by averaging over the gauge?eld,one obtains a sum of all the multi-loop diagrams with no couplings between the fermion polarization insertions into the gauge?eld propagators and the open fermion line corresponding to the fermion’s propagation between the space-time points x and y.Likewise,in the case of a generic multi-fermion amplitude,the allowed graphs can only contain open fermion lines which connect the incoming and outgoing asymptotical fermionic states,provided that the fermion polarization has already been absorbed into the gauge?eld propagator.

This approach can be viewed as a systematic improvement of the celebrated Bloch-Nordsieck model where all the spin-related e?ects are ignored which makes this model exactly soluble but restricts its applicability to the infrared (IR)regime|p2?m2|?m2near the fermion’s mass shell.

We emphasize that the IR regime can only exist if the fermions are massive,while in the massless case the entire region below the upper cuto?Λ(which is set by the conditions of the applicability of the e?ective QED-like description itself)falls into the opposite,ultraviolet(UV),regime which,in the case of a?nite fermion mass,is de?ned as |p2?m2|?m2.

The rest of the paper is organized as follows.We?rst describe the Schwinger’s functional technique and inves-tigate both the IR and UV asymptotics of the ordinary(gauge-dependent)fermion Green function in the general

D-dimensional case.Then,after having compared our general formulas with the well known3D results as well as with the partially known2D ones,we proceed with the gauge-invariant fermion amplitude proposed in Ref.[4]and ascertain its true behavior.We conclude our analysis with a discussion of the alternatives to the previously suggested form of the physical electron propagator as well as to the?ts to the ARPES data[13]exploiting the QED2+1-related scenarios.

II.FUNCTIONAL INTEGRAL REPRESENTATION OF FERMION AMPLITUDES

The conventional fermion Green function is given by the(properly normalized)functional integral over the fermion and gauge?eld con?gurations

G(x,y)=<Ψ(x)Ψ]D[Ψ]D[A]Ψ(x)Ψ,A])(5) Upon integrating the fermions out,one arrives at the expression

G(x,y)= D[A]G(x,y|A)exp(iS eff[A])(6) where the e?ective action of the gauge?eld includes the fermion polarization

S eff[A]=1

det[i???m]

q2+Π(q)(δμν+(λ?1)

qμqν

In this expression,the terms which are odd in A (z )contribute to the gauge invariant (see below)part of the mass operator

M (s |v )=

d q (2π)D +1D μν(q ) s

0dτ1 τ10dτ2(2v μ(τ1)+2p μ+σμαq α)(2v ν(τ2)+2p ν?σνβq β)

e 2i pq (τ1?τ2)+2i τ1τ2qv (τ3)dτ3(13)

In the above expressions,the integrations over the proper time parameters τi are ordered according to the order of their appearance in the products of the non-commutative factors (2v μ(τi )+2p μ±σμνq ν).

III.INFRARED BEHA VIOR

By using Eqs.(11-13)one can readily determine the IR behavior of the fermion Green function.With its momentum satisfying the condition |p 2?m 2|?m 2a fermion behaves as a heavy particle whose velocity remains essentially unchanged atfer emitting and absorbing an arbitrary number of the gauge ?eld quanta.Therefore,the Green function receives its main contribution from the fermion trajectories close to the straight-line path (which only coincides with the semiclassical trajectory in the case of a time-like separation between the ending points (x ?y )2>0).

This allows one to neglect the ?uctuations of the total fermion’s momentum with respect to its average value p ,in which case the mass operator introduces only a small correction

M IR (s |v )=i d q qp =?p O (1m 2

??p (14)In deriving (14)we took into account that a characteristic value of the parameter s ～|p 2?m 2|?1is determined by Eq.(11)and the fact that the integral (14)receives its main contribution from small transferred momenta q <～1/sp ～|p 2?m 2|/p ?p .In contrast,the integrals over τi in the gauge-dependent IR phase factor are formally divergent.They must be tackled by ?rst computing the momentum integral and then applying the so-called ”ribbon”regularization [11]p (τ1?τ2)→p (τ1?τ2)+l with (pl )=0and |l |=1/Λwhich yields the expression

ΦIR (s )=4

d q |p (τ1?τ2)+l |2?2(λ?1)p 4(τ1?τ2)2

2(sp Λ)?ln(sp Λ))?2(λ?1)(

π(p 2?m 2+iδ)1?ηIR /2

(16)which,near the mass shell,exhibits the anticipated algebraic behavior (3)with the IR anomalous dimension

ηIR =2g 2I D (λ?D )

(17)where

I D =[2D π(D +1)/2Γ((D +1)/2)]?1

(18)

Thus,in the3D case of the conventional weakly coupled QED3+1we recover the well-known IR exponent(see,e.g., [14])

η3D IR=

N q2)(21) Instead of the bare coupling g,it is1/N that now becomes a parameter of the perturbative expansion.We note that above the momentum scale Ng2no further logarithmic corrections are generated,so that the latter is now playing the role of the UV cuto?.Nonetheless,for the sake of uniformity of our presentation,in the following discussion we will continue using the notationΛand the label UV for the range of momenta m?q<～Λ=Ng2.

It is also worth mentioning that,owing to the parity conserving structure of the reducible four-fermion representa-tion,the radiative corrections generate no Chern-Simons terms.

Using(21)we obtain a coupling-independent anomalous exponent

η2D IR=

(23)

where= D[v]e?i v2dτF[v].

Eq.(23)has been extensively used,e.g.,in implementing the Feynman’s variational principle in the polaron and related problems.Expanding(11)to the?rst order in Dμν(q)we obtain

δ1G UV(p)=?i ∞0dse is(p2+iδ)[+i?p<ΦUV(s)>](24) The functionally averaged mass operator(12)is now determined by the transferred momenta q?p～1/

√

(2π)D+1Dμν(q)1?e is(q2+2qp)

D+1

ln(sΛ2)+ (25)

Notably,Eq.(25)is independent of the gauge parameter.In contrast,the averaged phase factor(13)which can be calculated in the p→0limit

<ΦUV(s)>= d q

(q2+2qp)2

(qμ+2pμ+σμαqα)(qν+2pν?σνβqβ)?isδμν]=i

(2π)D+1Dμν(q)[

1?e is(q2+2qp)

(q2+2qp)2

(qμ+2pμ+σμαqα)(qν+2pν?σνβqβ)?i?p sδμν]

=g2

I D(

D(3?D)

)+ (27)

By using the identity

?pγμ(?p+?q)γν?p=?p(qμ+2pμ+σμαqα)(qν+2pν?σνβqβ)?γμp2(qν+2pν?σνλqλ)?δμν?p(p+q)2

and integrating in(27)over the proper time s prior to the momentum integration one can also check that the correction given by Eq.(27)exactly reproduces the one-loop result of the conventional diagrammatic expansion

δ1G UV(p)=?i d q p4(p+q)2?pγμ(?p+?q)γν?p(28)

Instead of expanding Eq.(11)to higher orders in Dμν(q)one can perform summation of the leading(g2lnΛ)n terms by virtue of the standard renormalization group equation which,re?ects the scaling properties of a generic two-point amplitude(gauge invariant and non-invariant alike)under the change of the upper cuto?[14]

[Λ?

??g

+η(?g)]?p G UV(p;Λ;?g)=0(29)

where the leading order dependence of the anomalous dimension of the fermion Green function on the renormalized coupling strength?g is given by the explicit form of the?rst order correction(27)

η(g)=?Λ

D+1

)(31)

Further corrections to Eq.(31)require one not only to extract the subleading corrections of order g2n lnΛfrom the n th-order terms in the expansion of Eq.(11)in powers of v(s)and account for the improved fermion polarizationΠ(q) but also to proceed beyond the quenched approximation(7)for the e?ective action of the gauge?eld.

In the weakly-coupled3D case Eq.(31)reproduces the well known result[14]

η3D UV=

3π2N

(3λ?2),(33) in agreement with the result obtained in[15].

V.GAUGE INV ARIANT FERMION AMPLITUDE

After having tested our formalism against the known examples,we turn to the proposed candidate for the physical electron propagator which is given by Eq.(2)with the straight-line contourΓ

G|inv(x,y)= D[A]G(x,y|A)exp(i x y dzμAμ(z))exp(iS eff[A])(34)

Proceeding by analogy with the derivation presented in Section II,one readily obtains Eq.(11)where Eqs.(12)and (13)are replaced,respectively,with

M inv(s|v)= d q

](35) and

Φinv(s|v)= d q

s τ3 0

dτ4

e2i pq(s?τ1)+2i sτ1qv(τ4)dτ4?2i pqτ3?2iτ3/s s0qv(τ5)dτ5](36)

In the IR regime the path integration can still be carried out exactly by simply neglecting v(s)with respect to the average fermion’s momentum p.In the same approximation as that used in Section III(which is only justi?ed in the vicinity of the mass shell,provided that m=0),one readily obtains

M inv,IR(s)=2 d q

(2π)D+1Dμν(q)pμpν s

dτ1 τ10dτ2

[e2i pq(τ1?τ2)+2

dτ3e2i pq(s?τ1?τ3)]=0(38)

Thus,as?rst pointed out by the authors of Refs.[10],in the IR regime the gauge-invariant propagator(34)retains a simple pole

G|inv,IR(p)≈

?p+m

(2π)D+1

(q2+2qp)2(

p2q4

(2π)D+1g2

q2+2qp

[?p??q

D+1

ln(sΛ2)+ (42)

appears to coincide with Eq.(25).Thus,it is Eq.(42)that solely determines the correction to the gauge-invariant Green function

δ1G inv,UV(p)=?i ∞0dse is(p2+iδ)[+i?p<Φinv,UV(s)>]=2g2?p D+1ln(Λ2

q2+Π(q)[δμν+n2

qμqν

(nq)

](44)

Notably,the result(43)obtained with the use of Eq.(28)is independent of the direction of the vector n,for all the

terms proportional to?n(np)cancel out and only those proportional to?p remain in the?nal expression.

It is worth mentioning that the integrals in Eqs.(41,42)as well as in Eq.(28)with the gauge propagator(44)are

all plagued with the spurious poles,such as1/(qp)1,2.We handle these singular denominators by resorting to the

exponential integral representation:1/(qn)=?i ∞0ds exp(is(qn+iδ)).Then,after having performed the Lorentz-invariant momentum integration,we carry out the remaining integrals over the auxiliary parameter s with the use of

the”ribbon”regularization[11].This procedure yields the following logarithmic integrals appearing in our calculation

d q

q D?1(p+q)2(qn)=

iI D

ln(

Λ2

(2π)D+1qμqν

2nμnν?δμνn2

and

d q

q D+1(p+q)2(qn)=

iI D

n2?2

nμnνnλ

)

One can check that the above expressions are fully consistent with the standard”principal value”prescription for the spurious poles,whose advanced form is known in the?eld-theoretical literature as the Leibbrandt-Mandelstam rule (see[16]and references therein).

Finally,by invoking the renormalization group equation(29)we?nd that the logarithmic correction(43)tends to exponentiate,thereby resulting in the new UV anomalous dimension

ηinv,UV=?4g2I D

8π2

(46)

Nevertheless,we did?nd some comfort in comparing(46)with the exponent which had been previously found to control the power-law UV behavior of the non-abelian analogue of Eq.(34)in the SU(3)-symmetrical case[17]

η3D,SU(3) inv,UV =?

N N2?1

a=1

tr(T a T a)=

N2?1

3π2N

(49)

which is negative,contrary to the result of Ref.[4]and in agreement with the sign(albeit not the magnitude)of the exponent quoted without derivation in Ref.[5].However,it remains to be seen whether the exponentiation of

M UV

inv (s)as well as vanishing ofΦUV inv(s)still hold beyond the leading1/N order.

Lastly,by comparing Eqs.(31)and(45)one can also deduce the UV anomalous dimension of the exponential factor exp(i Aμdzμ)

ηexp,UV=?g2I D(D+λ)(50) Interestingly enough,forλ=?D this exponent equals zero,and the UV anomalous dimension of the non-invariant propagator coincides with(45),in agreement with the observation made in the3D non-abelian case[17].

VI.DISCUSSION

Our calculation demonstrates that in the massless case the gauge invariant Green function(34)appears to decay slower than the bare one,in a marked contrast with the previously conjectured Luttinger-like behavior.In this concluding Section,we make an attempt to rationalize these?ndings,although we refrain from making any?nal judgement on their physical implications.

Albeit somewhat counterintuitive,the found UV behavior is not totally incomprehensible.In fact,the generic behavior of an invariant fermion amplitude is manifested by the asymptotic formula

GΓinv(x)～exp(?C|x|Λ+ηln(|x|Λ))(51)

where C>0,and the expression(51)decays with|x|exponentially,regardless of the sign ofη,because the logarithmic term in the exponent is subleading to the linear one.However,in a renormalizable gauge theory where the gauge invariance is reinforced throughout the whole process of renormalization,the latter would be routinely cancelled out by counterterms,which leaves behind the logarithmic term of(potentially)either sign.

This situation would change,however,should one choose to relaxe the condition of renormalizability at the expense of the gauge invariance,since the radiative corrections to the action(1)generically produce a?nite mass of the vector ?eld Aμ.Loosely speaking,the situation would then resemble that in the Schwinger’s QED1+1where the gauge?eld acquires a mass M～g,and the analogue of Eq.(34)behaves as

G|inv(x)～exp(?

x at x?1/M,thus siggestingη1D inv=?1/2.

We mention,in passing,that the exponential,rather than a power-law,behavior has also been found in the problem of Dirac fermions in the presence of a static random vector potential(A(x)=(0, a( r)))which allows for an asymptotically exact solution in the ballistic regime of large fermion energies[18].

Conceivably,in some of the abovementioned physical applications of QED2+1with N=2the problem of the slow space-time decay of the gauge invariant amplitude(34)can be thwarted by a spontaneous development of a?nite fermion mass,in which case the behavior of G|inv(x)at large x will be governed by the(free)IR asymptotic(39) instead of the UV one.However,the intrinsic propensity of the2D Dirac fermions in QED2+1towards generating a ?nite mass(usually referred to as the phenomenon of chiral symmetry breaking)is believed to occur only at su?ciently small N

To this end,the authors of Refs.[7]conjectured that the critical value N c in the QED-like description of the quantum disordered planar d-wave superconductor may become greater than two due to the lack of rotational invariance.On the other hand,in the?nite-temperature counterpart of the2D chiral symmetry breaking transition in the(spatially) rotationally-invariant e?ective theory of a single layer of graphite N c was found to be further reduced as compared to the Lorentz-invariant case[9].

However,should one insist on maintaining both the gauge and Lorentz invariances of the renormalized gauge?eld action,the problem of the slow spatial decay of the alleged physical electron propagator(34)associated with its negative UV anomalous dimension(45)could not be resolved without re-examining the”minimal”form of this Green function.In fact,the task of constructing the proper gauge transformation which converts the auxiliary Dirac fermions into the physical electrons may not be limited to a particular choice of the contourΓin Eq.(2)but may also require one to modify the phase factor itself.

It is worth noting that in the previous calculations of the”zero-bias anomaly”in the tunneling density of states in the compressible Quantum Hall e?ect[12],the construction of the electron Green function,albeit seemingly given by the same Eq.(34)with the contourΓnow chosen along the temporal axis,was,in fact,more involved.Indeed,in the semiclassical approximation employed in[12],the gauge?eld dependence of the exponential factor exp(i dzμAμ) would have been exactly compensated by that of the non-gauge invariant Green function G(t, 0|A),thus making the functional average of the product of the two behave essentially as in the absence of any gauge coupling. Nevertheless,the electron density of states computed in[12]appeared to be strongly a?ected by the Chern-Simons gauge?uctuations which can be traced back to the fact that,in addition to the abovementioned factors,the electron Green function happened to contain yet another factor,the exponent of the saddle-point value of the e?ective action of the Chern-Simons gauge?eld.It was,in fact,this factor which was solely responsible for the strong suppression of the tunneling density of states,consistent with the physical interpretation of the Chern-Simons?eld as representing the e?ect of the Coulomb coupling in the presence of strong magnetic?eld.In light of the fact that in the problem at hand the time reversal symmetry remains unbroken,no such an additional factor can be readily incorporated into the naive form of the electron propagator(34).

In order to further elaborate on this point,we mention yet another example demonstrating the sensitivity of a generic gauge invariant amplitude to the details of its construction.To this end,we recall the original Dirac’s idea of explicitly constructing a”dressed charge”corresponding to a physical electron by means of the gauge transformation

Ψphys(x)=exp(i d yχμ(x?y)Aμ(y))Ψ(x)(53)

where the vector functionχμ(x)obeys the equation?μχμ(x)=δ(x).In the time-independent Shrodinger operator rep-resentation,the originally proposed transformation from the bare fermions to the physical electrons was implemented as a space-like Dirac string between the location of the fermion and an in?nitely remote point

χ0=0,χi=< x|

Ψphys(y)>is IR?nite(see Eq.(39))and undergoes multiplicative UV renormalization at a single point pμ=(m, 0)on the mass shell corresponding to a static charge [16],in agreement with the general expectation that the absence of any singularity other than a simple pole is characteristic of the propagator of an exact eigenstate with the quantum numbers of electron.

It was shown in[16]that in the case of a dressed charge moving with a?nite velocity u the above phase factor needs to be further modi?ed

Ψphys(x| u)=exp(iγ d D?1 y⊥dy < x|1

1? u2and both the parallel and perpendicular components of A are determined with respect to the velocity vector.As shown in[16],Eq.(54)gives rise to the operator whose propagator is both IR-?nite and UV-renormalizable at pμ=mγ(1, u).

Such a strong dependence on the exact details of the construction of the phase factor appearing in the gauge transformation(53)indicates that the true electron Green function may well be quite di?erent from Eq.(34).In particular,it remains to be seen whether one can at all?nd an alternate form GΓinv(x)which would decay faster than the bare propagator.Given the intellectual appeal of the QED2+1picture,such an endevour is de?nitely worth the e?ort,and a further investigation into this possibility is currently under way.

Should,however,the sought-after Luttinger-like behavior fail to occur even in the modi?ed prototype of the electron propagator,one can still consider an alternative approach to the quantum disordered d-wave systems,e.g.,the one that was put forward in the context of the scenario of a second pairing transition in the2D superconducting phase[20].In [21],apart from fully idenifying the true nature of this transition and its critical properties(the speci?c predictions of Ref.[21]for the critical exponents are roughly consistent with the recent tunneling data in Ca-doped Y BaCuO[22]), it was further speculated that it might be possible to extend the e?ective Higgs-Yukawa theory of the nodal fermion excitations coupled to the?uctuations of the secondary order parameter of either id xy or is symmetry well into the pseudogap phase.Rather than a global superconducting coherence,this would only require the presence of a local parent d x2?y2-wave order.If this speculation prove valid,it can provide a viable alternative to the QED2+1-based?ts to the ARPES data[4,6],since in the Higgs-Yukawa theory the anomalous dimension of the Dirac fermions is indeed positive[20,21,23].

To summarize,in the present paper we applied the Schwinger’s functional integral representation of the fermion amplitudes to the analysis of both the infrared and ultraviolet asymptotics of the conventional(non-gauge invariant) fermion Green function and a particular gauge-invariant amplitude(34).

In the IR regime,this method provides a substantial improvement with regard to the spinless Bloch-Nordsieck model or the customary semiclassical(eikonal)approximation,since it preserves the exact spinor structure of the fermion amplitudes.Moreover,the intrinsic”exponential”form of the Schwinger’s integral representation facilitates truly non-perturbative calculations.

In the opposite,UV,regime,the method allows one to naturally separate between the gauge invariant and non-invariant contributions to the mass operator and systematically compute the higher order contributions into both kinds of terms.For a speci?c class of problems,including the amplitudes given by Eq.(2),it has a signi?cant advantage as compared to the conventional diagrammatic technique which is not particularly well suited for such calculations,for the very rules of the diagrammatic expansion turn out to be amplitude-speci?c and depend on a particular choice of the contourΓ[16].

To our surprise,the previously suggested”minimal”form of the physical electron Green function(34)was found to manifest a negative anomalous dimension,contrary to the much-anticipated Luttinger liquid behavior.The impli-cations of this observation were discussed,some of them pertaining to the applicability of Eq.(34)and other to the possible alternatives to the QED2+1-like description of the ARPES data in the high-T c cuprates.

The author acknowledges valuable discussions and email communications with T.Appelquist,D.Dyakonov,A. Luther,N.Mavromatos,K.Martin,J.Ng,N.Stefanis,Z.Tesanovic,and A.Yashenkin.This research was supported by the NSF under Grant No.DMR-0071362and also by the Aspen Center for Physics,ICTP(Trieste),and Nordita (Copenhagen)where part of this work was carried out.

中外鞋码对照表

鞋码对照表,中国/美国/国际鞋码对照表鞋码，通常也称鞋号，是用来衡量人类脚的形状以便配鞋的标准单位系统。目前世界各国采用的鞋码并不一致，但一般都包含长、宽两个测量。长度是指穿者脚的长度，也可以是制造者的鞋楦长。即使在同一个国家/地区，不同人群和不同用途的鞋，例如儿童、运动鞋，也有不同的鞋码定义。下面是尺码对照表，可以帮你解决如何挑选正确的码数；经过量度脚长与脚宽，让你能够挑选到合适的鞋子。国际标准鞋号表示的是脚长的毫米数。中国标准采用毫米数或厘米数。如：245是毫米数，24 1/2是厘米数，表示一样的尺码。换算公式：厘米数×2－10=欧制（欧制+10）÷2=厘米数厘米数－18+0.5=美制美制+18－0.5=厘米数厘米数－18－0.5=英制英制+18+0.5=厘米数（欧码+10）×5=中国鞋号，如欧码35的鞋，对应的中国鞋号为225；欧码37对应的中国鞋号为235。鞋号换算表（单位：毫米）34号——22035号——22536号——23037号——23538号——24039号——24540号——25041号——25542号——26043号——26544号——27045号——275。男人鞋尺码对照表：厘米24.5 24.5 25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30 30.5 31 中国码38.5 39 40 40.5 41 42 42.5 43 44 44.5 45 45.5 46 47 47.5 英国码 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 美国码 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13

各国钢号对照表

[正文] 一、我国钢号表示方法概述钢的牌号简称钢号，是对每一种具体钢产品所取的名称，是人们了解钢的一种共同语言。我国的钢号表示方法，根据国家标准《钢铁产品牌号表示方法》（G B221-79）中规定，采用汉语拼音字母、化学元素符号和阿拉伯数字相结合的方法表示。即： ①钢号中化学元素采用国际化学符号表示，例如S i,M n,C r……等。混合稀土元素用“R E”（或“X t”）表示。 ②产品名称、用途、冶炼和浇注方法等，一般采用汉语拼音的缩写字母表示，见表。 ③钢中主要化学元素含量（%）采用阿拉伯数字表示。表：G B标准钢号中所采用的缩写字母及其涵义名称汉字符号字体位置屈服点屈Q 大写头沸腾钢沸 F 大写尾半镇静钢半 b 小写尾镇静钢镇Z 大写尾特殊镇静钢特镇TZ 大写尾氧气转炉（钢）氧Y 大写中碱性空气转炉（钢）碱J 大写中易切削钢易Y 大写头碳素工具钢碳T 大写头滚动轴承钢滚G 大写头焊条用钢焊H 大写头高级（优质钢）高 A 大写尾特级特 E 大写尾铆螺钢铆螺ML 大写头锚链钢锚M 大写头矿用钢矿K 大写尾汽车大梁用钢梁L 大写尾压力容器用钢容R 大写尾多层或高压容器用钢高层gc 小写尾铸钢铸钢ZG 大写头

轧辊用铸钢铸辊ZU 大写头地质钻探钢管用钢地质DZ 大写头电工用热轧硅钢电热DR 大写头电工用冷轧无取向硅钢电无DW 大写头电工用冷轧取向硅钢电取DQ 大写头电工用纯铁电铁DT 大写头超级超 C 大写尾船用钢船 C 大写尾桥梁钢桥q 小写尾锅炉钢锅g 小写尾钢轨钢轨U 小写头精密合金精J 大写中耐蚀合金耐蚀NS 大写头变形高温合金高合GH 大写头铸造高温合金K 大写头二、我国钢号表示方法的分类说明 1．碳素结构钢 ①由Q+数字+质量等级符号+脱氧方法符号组成。它的钢号冠以“Q”，代表钢材的屈服点，后面的数字表示屈服点数值，单位是M P a例如Q235表示屈服点（σs）为235M P a的碳素结构钢。 ②必要时钢号后面可标出表示质量等级和脱氧方法的符号。质量等级符号分别为A、B、C、D。脱氧方法符号：F表示沸腾钢；b表示半镇静钢：Z表示镇静钢；T Z表示特殊镇静钢，镇静钢可不标符号，即Z和T Z都可不标。例如Q235-A F表示A 级沸腾钢。 ③专门用途的碳素钢，例如桥梁钢、船用钢等，基本上采用碳素结构钢的表示方法，但在钢号最后附加表示用途的字母。 2．优质碳素结构钢 ①钢号开头的两位数字表示钢的碳含量，以平均碳含量的万分之几表示，例如平均碳含量为0.45%的钢，钢号为“45”，

各种单位换算及公式

各种单位换算及公式长度单位面积单位 1 in = 25.4 mm 1 in 2 = 6.45 cm2 1 ft = 0.3048 m 1 ft2 = 0.09 3 m2 1 micron = 0.001 mm 体积单位 1 litre = 0.001 m3 1 cu.ft. = 0.0283 m3 1 cu.in. = 16.39 cm3 1 fluid oz.(imp) = 28.41 mL 1 fluid oz.(us) = 29.57 mL 1 gal(imp) = 4.546 L 1 gal(us) = 3.79 L 温度单位 (°F-32)X5/9=℃K-273.15 = ℃ 功及能量单位 1 Nm = 1 J 1 kgm = 9.807 J 1 kW/hr = 3.6 MJ 1 lbft = 1.356 J 功率单位 1 Nm/sec = 1 W 1 lbft/sec = 1.356 W 1 kgm/sec = 9.807 W 1 Joule/sec = 1 W 1 H.P.(imp) = 745.7 W 质量单位 1 lb = 453.6 g 1 tonne = 1000 kg 1 ton(imp) = 1016 kg 1 ton(us) = 907. 2 kg

流量计算公式 Q = Cv值X 984 = Kv值X 1100 Cv = So ÷ 18 力单位 1 kgf = 9.81 N 1 lbf = 4.45 N 1 kp(kilopound) = 9.81 N 1 poundal = 138.3 mN 1 ton force = 9.964 kM 力矩单位 1 kgm = 9.807 Nm 1 ft. poundal = 0.0421 Nm 1 in lb = 0.113 Nm 1 ft lb = 1.356 Nm 压力单位 1 psi = 6.89 kPa 1 kgf/cm 2 = 98.07 kPa 1 bar = 100 kPa 1 bar = 14.5 psi 1 mm mercury = 133.3 Pa 1 in mercury = 3.39 kPa 1 Torr = 133.3 Pa 1 ft water = 0.0298 bar 1 bar = 3.33 ft water 1 atmosphere = 101.3 kPa 1 cm water = 97.89 Pa 1 in water = 248.64 Pa 换算表 1psi=6.895kPa=0.07kg/cm2=0.06895bar=0.0703atm 1standard atmosphere=14.7psi=101.3kPa=1.01325bar 1kgf/cm2 = 98.07kPa=14.22psi = 28.96ins mercury 1m3 = 1000000cm3 1cu ft/min = 28.3 l/min

世界钢号对照表

一、我国钢号表示方法概述钢的牌号简称钢号，是对每一种具体钢产品所取的名称，是人们了解钢的一种共同语言。我国的钢号表示方法，根据国家标准《钢铁产品牌号表示方法》（GB221-79）中规定，采用汉语拼音字母、化学元素符号和阿拉伯数字相结合的方法表示。即： ①钢号中化学元素采用国际化学符号表示，例如Si,Mn,Cr……等。混合稀土元素用“RE”（或“Xt”）表示。 ②产品名称、用途、冶炼和浇注方法等，一般采用汉语拼音的缩写字母表示，见表。 ③钢中主要化学元素含量（%）采用阿拉伯数字表示。表：GB标准钢号中所采用的缩写字母及其涵义

二、我国钢号表示方法的分类说明 1．碳素结构钢 ①由Q+数字+质量等级符号+脱氧方法符号组成。它的钢号冠以“Q”，代表钢材的屈服点，后面的数字表示屈服点数值，单位是MPa例如Q235表示屈服点（σs）为235 MPa的碳素结构钢。 ②必要时钢号后面可标出表示质量等级和脱氧方法的符号。质量等级符号分别为A、B、C、D。脱氧方法符号：F表示沸腾钢；b表示半镇静钢：Z表示镇静钢；TZ表示特殊镇静钢，镇静钢可不标符号，即Z和TZ都可不标。例如Q235-AF表示A级沸腾钢。 ③专门用途的碳素钢，例如桥梁钢、船用钢等，基本上采用碳素结构钢的表示方法，但在钢号最后附加表示用途的字母。 2．优质碳素结构钢 ①钢号开头的两位数字表示钢的碳含量，以平均碳含量的万分之几表示，例如平均碳含量为0.45%的钢，钢号为“45”，它不是顺序号，所以不能读成45号钢。 ②锰含量较高的优质碳素结构钢，应将锰元素标出，例如50Mn。 ③沸腾钢、半镇静钢及专门用途的优质碳素结构钢应在钢号最后特别标出，例如平均碳含量为0.1%的半镇静钢，其钢号为10b。 3．碳素工具钢 ①钢号冠以“T”，以免与其他钢类相混。 ②钢号中的数字表示碳含量，以平均碳含量的千分之几表示。例如“T8”表示平均碳含量为0.8%。 ③锰含量较高者，在钢号最后标出“Mn”，例如“T8Mn”。 ④高级优质碳素工具钢的磷、硫含量，比一般优质碳素工具钢低，在钢号最后加注字母“A”，以示区别，例如 “T8MnA”。 4．易切削钢 ①钢号冠以“Y”，以区别于优质碳素结构钢。 ②字母“Y”后的数字表示碳含量，以平均碳含量的万分之几表示，例如平均碳含量为0.3%的易切削钢，其钢号为“Y30”。 ③锰含量较高者，亦在钢号后标出“Mn”，例如“Y40Mn”。 5．合金结构钢 ①钢号开头的两位数字表示钢的碳含量，以平均碳含量的万分之几表示，如40Cr。 ②钢中主要合金元素，除个别微合金元素外，一般以百分之几表示。当平均合金含量＜1.5%时，钢号中一般只标出元素符号，而不标明含量，但在特殊情况下易致混淆者，在元素符号后亦可标以数字“1”，例如钢号“12CrMoV”和“12Cr1MoV”，前者铬含量为0.4-0.6%，后者为0.9-1.2%，其余成分全部相同。当合金元素平均含量≥1.5%、≥2.5%、≥3.5%……时，在元素符号后面应标明含量，可相应表示为2、3、4……等。例如18Cr2Ni4WA。 ③钢中的钒V、钛Ti、铝AL、硼B、稀土RE等合金元素，均属微合金元素，虽然含量很低，仍应在钢号中标出。例如20MnVB钢中。钒为0.07-0.12%，硼为0.001-0.005%。 ④高级优质钢应在钢号最后加“A”，以区别于一般优质钢。 ⑤专门用途的合金结构钢，钢号冠以（或后缀）代表该钢种用途的符号。例如，铆螺专用的30CrMnSi钢，钢号表示为ML30CrMnSi。 6．低合金高强度钢 ①钢号的表示方法，基本上和合金结构钢相同。 ②对专业用低合金高强度钢，应在钢号最后标明。例如16Mn钢，用于桥梁的专用钢种为“16Mnq”，汽车大梁的专用钢种为“16MnL”，压力容器的专用钢种为“16MnR”。 7．弹簧钢弹簧钢按化学成分可分为碳素弹簧钢和合金弹簧钢两类，其钢号表示方法，前者基本上与优质碳素结构钢相同，后者基本上与合金结构钢相同。 8．滚动轴承钢 ①钢号冠以字母“G”，表示滚动轴承钢类。 ②高碳铬轴承钢钢号的碳含量不标出，铬含量以千分之几表示。例如GCr15。渗碳轴承钢的钢号表示方法，基本上和合金结构钢相同。 9．合金工具钢和高速工具钢

各国尺码对照表

敦煌网分享外贸知识：各国尺码对照表Women's Clothing Size Conversions女装尺寸转化 Women's Dresses and Suits (Misses Sizes)女式礼服和套装（年轻女士尺寸） Women's Dresses and Suits (Junior Sizes)女式礼服和套装（少女尺寸） Women's Blouses & Sweaters 女式衬衣和毛衣 US Women's Size Standards美国女式尺寸标准 Women's Bra Sizes 女式胸罩尺寸 Women's Shoes 女式鞋码 Men's Clothing Size Conversions 男式服装尺寸

Men's Suits, Coats and Sweaters 男式西服，大衣和毛衣 1.The US size may be followed by a letter designation 美国尺寸按字母区分 2.(S = Short, R = Regular, L = Long) S=短款 R=均码 L=长款 Men's Dress Shirts 男式衬衫 The US collar size may be followed by a sleeve length in inches 32 - 35. 美国的衣领尺寸按照袖子长度的标准，在32-25英寸之间 Men's Pants 男式裤子 Two numbers indicating waist size, and inseam lengths of 28 - 35. 28-35这两个数字表明了腰围和裤腿长度 US Men's Size Standards 美国男式尺寸标准 (Approximate 估算的) Men's Hat Sizes 男式帽子尺寸 Many hats are sized only XS, S, M, L, XL. 男式帽子尺寸只有XS,S ,M,K,XL

尺码对照表~衣服、裤子、鞋大小尺寸

服装尺码对照表版权说明：本文由宏业服装整理编辑，未经同意，复制、转载、摘编追究法律责任服装尺码对照表也被人们称为服装尺寸表，是表示人体外形及服装量度的一系列规格参数，是为了规范服装厂商生产及方便顾客选购而形成的一套度量指标。其中有很多参数，这些参数比较复杂，主要是对于专业人士应用而规定的，如厂家；对于服装买家而言，就不用了解其中详细了，只要了解自己和身边少数亲朋好友的尺寸就够用了。这里我司专门设立一个栏目，用来详细列出各类服装的尺码表，给大家参考对比之用。这个服装尺码对照表仅供大家参考之前。另外，因为我国地域广阔，人员十多亿，东南西北生活水平各异，体型就有一定出入，大家应该将平时所购服装的尺码也纳入参考数据，这样我们就能力求服装的准确性。女装（外衣、裙装、恤衫、上装、套装）

男装（外衣、恤衫、套装）男装（衬衫）男装（裤装）

服装,裤子,男女鞋,尺码对照表服装尺码对照表

29码＝尺腰=73.5CM 30码＝尺腰=77CM 31码＝尺腰=80CM 32码＝尺腰=83.5CM 33码＝尺腰=87CM 34码＝尺腰=90CM 36码＝尺腰 38码＝尺腰 40码＝尺腰裤子尺码对照表 26号------1尺9寸臀围2尺6 32号------2尺6寸臀围3尺2 27号------2尺0寸臀围2尺7 34号------2尺7寸臀围3尺4

28号------2尺1寸臀围2尺8 36号------2尺8寸臀围3尺5-6 29号------2尺2寸臀围2尺9 38号------2尺9寸臀围3尺7-8 30号------2尺3寸臀围3尺0 40号------3尺0寸臀围3尺9-4尺 31号------2尺4寸臀围3尺1 42号------3尺1-2寸臀围4尺1-2 裤子尺码对照表

压力单位换算方法

工程上常用的是兆帕（MPa）：1MPa=1000000Pa。 1个标准大气压力=1.00336×0.098MPa=0.10108MPa≈0.1Mpa。 1bar=0.1MPa 压力的法定单位是帕斯卡（Pa）：1Pa=1N/㎡（牛顿/平方米）。压力单位换算： 1MPa=1000kPa 1kPa=10mbar=101.9716 mmH2O = 4.01463imH2O 10mWC＝1bar＝100kPa bar 巴= 0.987 大气压= 1.02 千克/平方厘米= 100 千帕= 14.5 磅/平方英寸 PSI英文全称为Pounds per square inch。P是磅pound，S是平方square，I是英寸inch。把所有的单位换成公制单位就可以算出：1bar≈14.5psi 1psi=6.895kPa=0.06895bar

1兆帕(MPa)=145磅/英寸2(psi)=10.2千克/厘米2(kg/cm2)=10巴(bar)=9.8大气压(atm) 1磅/英寸2(psi)=0.006895兆帕(MPa)=0.0703千克/厘米2(kg/cm2)=0.0689巴(bar)=0.068大气压(atm) 1巴(bar)=0.1兆帕(MPa)=14.503磅/英寸2(psi)=1.0197千克/厘米 2(kg/cm2)=0.987大气压(atm) 1大气压(atm)=0.101325兆帕(MPa)=14.696磅/英寸2(psi)=1.0333千克/厘米2(kg/cm2)=1.0133巴(bar) ------------------------------------------------------------------------------------- 压力单位换算方法 1. 1atm=0.1MPa=100KPa=1公斤=1bar=10米水柱＝14.5PSI 2.1KPa=0.01公斤 =0.01bar=10mbar=7.5mmHg=0.3inHg=7.5torr=100mmH2O=4inH2O 3. 1MPa=1N/mm2 14.5psi=0.1Mpa 1bar=0.1Mpa 30psi=0.21mpa,7bar=0.7mpa 现将单位的换算转摘如下： Bar---国际标准组织定义的压力单位。 1 bar=100,000Pa 1Pa=F/A, Pa: 压力单位, 1Pa=1 N/㎡ F : 力, 单位为牛顿(N) A: 面积, 单位为㎡ 1bar=100,000Pa=100Kpa 1 atm=101,325N/㎡=101,325Pa 所以,bar是一种表压力(gauge pressure)的称呼。

AWG-标准线径对照表

AWG 标准线径对照表线径的粗细是以号数(xxAWG)来表示的，数目越小表示线径愈粗，所能承载的电流就越大，反之则线径越细，耐电流量越小。例如说：12号的耐电流量是20安培，最大承受功率是2200瓦，而18号线的耐电流量则是7安培，最大承受功率是770瓦。为什么AWG号数越小直径反而越大？如这么解释你就会明白，固定的截面积下能塞相同的AWG线的数量，如11#AWG号数可塞11根而15#AWG号数可塞15根，自然的15#AWG的单位线径就较小。美规线径值单一导体或群导体【各正值或负值】的线径值(Gauge)是以圆或平方厘米(mm2) 量测而得，平方厘米不常用在量测线径值，由于牵涉到不正确，因一般大部份的导体形体，包含长方形及其他怪异形状。因此我们拿全部的量测以圆平方厘米(c/m)为参考值群导体计算的方法或公式：加上单一导体的线径值总和，并比较上表求得。如果值落入两者之间，取比较少的值。 40股群导体线的线径值为，如每一芯为24 Guage = 40 x 405 c/m = 16，200 c/m = 9 AWG(得出值落入12960c/m和16440c/m之间) 快速求得线径值的方法：两条(AWG)相加时，该单一线径值减3. ex. 2 x 18 AWG = (18-3=) 15 AWG 三条(AWG)相加时，该单一线径值减5. ex. 3 x 24 AWG = (24-5=) 19 AWG 四条(AWG)相加时，该单一线径值减6. ex. 4 x 10 AWG = (10-6=) 04 AWG 请记得“快速求得线径值的方法”一些案例也许边际会不正确，只采用此方式为大原则 AWG 标准线径规格对照表

美国-中国-国际鞋码对照表

鞋码，通常也称鞋号，是用来衡量人类脚的形状以便配鞋的标准单位系统。目前世界各国采用的鞋码并不一致，但一般都包含长、宽两个测量。长度是指穿者脚的长度，也可以是制造者的鞋楦长。即使在同一个国家/地区，不同人群和不同用途的鞋，例如儿童、运动鞋，也有不同的鞋码定义。下面是尺码对照表，可以帮你解决如何挑选正确的码数；经过量度脚长与脚宽，让你能够挑选到合适的鞋子。国际标准鞋号表示的是脚长的毫米数。中国标准采用毫米数或厘米数。如：245是毫米数，24 1/2是厘米数，表示一样的尺码。换算公式：厘米数×2－10=欧制（欧制+10）÷2=厘米数厘米数－18+0.5=美制美制+18－0.5=厘米数厘米数－18－0.5=英制英制+18+0.5=厘米数（欧码+10）×5=中国鞋号，如欧码35的鞋，对应的中国鞋号为225；欧码37对应的中国鞋号为235。鞋号换算表（单位：毫米）34号——22035号——22536号——23037号——23538号——24039号——24540号——25041号——25542号——26043号——26544号——27045号——275。男人鞋尺码对照表：厘米24.5 24.5 25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30 30.5 31 中国码38.5 39 40 40.5 41 42 42.5 43 44 44.5 45 45.5 46 47 47.5 英国码 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 美国码 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 女人鞋尺码对照表：厘米22 22 22.5 23 23.5 24 24.5 25 25.5 26 26.5 27 27.5 28 28.5 29 30 30.5 中国码35 35.5 36 36.5 37.5 38 38.5 39 40 40.5 41 42 42.5 43 44 44.5 45.5 46 英国码 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10.5 11 美国码 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 13 13.5

各种单位换算及公式

各种单位换算及公式长度单位面积单位 1 in = 25.4 mm 1 in 2 = 6.45 cm2 1 ft = 0.3048 m 1 ft 2 = 0.09 3 m2 1 micro n = 0.001 mm 体积单位 1 litre = 0.001 m3 1 cu.ft. = 0.0283 m3 1 cu.i n. = 16.39 cm3 1 fluid oz. (imp) = 28.41 mL 1 fluid oz. (us) = 29.57 mL 1 gal(imp) = 4.546 L 1 gal(us) = 3.79 L 温度单位 (°-32)X5/9= C K-273.15 = C 功及能量单位 1 Nm = 1 J 1 kgm = 9.807 J 1 kW/hr = 3.6 MJ 1 Ibft = 1.356 J 功率单位 1 Nm/sec = 1 W 1 lbft/sec = 1.356 W 1 kgm/sec = 9.807 W 1 Joule/sec = 1 W 1 H.P.(imp) = 745.7 W

质量单位 1 to nne = 1000 kg 1 lb = 453.6 g

流量计算公式 Q = Cv 值X 984 = Kv 值X 1100 Cv = So 48 力单位 1 kgf = 9.81 N 1 Ibf = 4.45 N 1 kp(kilopou nd) = 9.81 N 1 pou ndal = 138.3 mN 1 ton force = 9.964 kM 力矩单位 1 kgm = 9.807 Nm 1 ft. poun dal = 0.0421 Nm 1 in lb = 0.113 Nm 1 ft lb = 1.356 Nm 压力单位 1 psi = 6.89 kPa 1 kgf/cm 2 = 98.07 kPa 1 bar = 100 kPa 1 bar = 14.5 psi 1 mm mercury =133.3 Pa 1 in mercury =3.39 kPa 1 Torr = 133.3 Pa 1 ft water = 0.0298 bar 1 bar = 3.33 ft water 1 atmosphere = 101.3 kPa 1 cm water = 97.89 Pa 1 in water = 248.64 Pa 换算表 1psi=6.895kPa=0.07kg/cm2=0.06895bar=0.0703atm 1sta ndard atmosphere=14.7psi=101.3kPa=1.01325bar 1kgf/cm2 = 98.07kPa=14.22psi = 28.96i ns mercury 1m3 = 1000000cm3

常用线规号码与线径对照表

线规SWG BWG BG AWG 号码英寸毫米英寸毫米英寸毫米英寸毫米 7／0 6／0 5／0 4／0 3／0 2／0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0．500 0．464 0．432 0．400 0．372 0．348 0．324 0．300 0．276 0．252 0．232 0．212 0．192 0．176 0．160 0．144 0．128 0．116 0．104 0．092 0．080 0．072 0．064 0．056 0．048 0．040 0．036 0．032 0．0280 0．0240 0．0220 0．0200 0．0180 12．700 11．786 10．973 10．160 9．449 8．839 8．230 7．620 7．010 6．401 5．893 5．385 4．877 4．470 4．046 3．658 3．251 2．946 2．642 2．337 2．032 1．829 1．626 1．422 1．219 1．016 0．914 0．813 0．711 0．610 0．559 0．508 0．457 -- -- 0．500 0．454 0．425 0．330 0．340 0．300 0．284 0．259 0．238 0．220 0．203 0．180 0．165 0．148 0．134 0．120 0．109 0．095 0．083 0．072 0．065 0．058 0．049 0．042 0．035 0．032 0．028 0．025 0．022 0．020 0．018 -- -- 12．700 11．532 10．795 9．652 8．639 7．620 7．214 6．579 6．045 5．588 5．156 4．572 4．191 3．759 3．404 3．048 2．769 2．413 2．108 1．829 1．651 1．473 1．245 1．067 0．839 0．813 0．711 0．635 0．559 0．508 0．457 0．6666 0．6250 0．5883 0．5416 0．5000 0．1152 0．3954 0．3532 0．3147 0．2804 0．2500 0．2225 0．1981 0．1764 0．1570 0．1398 0．1250 0．1313 0．0991 0．0882 0．0785 0．0699 0．0625 0．0556 0．0495 0．0440 0．0392 0．0349 0．03125 0．02782 0．02476 0．02204 0．01961 16．932 15．875 14．943 13．757 12．700 11．308 10．069 8．971 7．993 7．122 6．350 5．652 5．032 4．481 3．988 3．551 3．175 2．827 2．517 2．240 1．994 1．775 1．588 1．412 1．257 1．118 0．996 0．887 0．794 0．707 0．629 0．560 0．498 -- 0．5800 0．5165 0．4600 0．4096 0．3648 0．3249 0．2893 0．2576 0．2294 0．2043 0．1819 0．1620 0．1443 0．1285 0．1144 0．1019 0．0907 0。0808 0．0720 0．0648 0．0571 0．0508 0．0453 0．0403 0．0359 0．0320 0．0285 0．02535 0．02010 0．01790 0．01594 0．01420 -- 14．732 13．119 11．684 10．404 9．266 8．252 7．348 6．544 5．827 5．189 4．621 4．115 3．665 3．264 2．906 2．588 2．305 2．053 1．828 1．628 1．450 1．291 1．150 1．024 0．912 0．812 0．723 0．644 0．573 0．511 0．455 0．405 常用线规号码与线径对照表

线材线号AWG与导线截面积对照表芯线

American Wire Gauge AWG mm2 42 0.003 1/0.06 41 0.004 1/0.07 40 0.005 1/0.08 38 0.008 1/0.10 36 0.013 1/0.127 34 0.020 1/0.16 7/0.06 32 0.032 1/0.203 7/0.08 8/0.07 11/0.06 30 0.051 1/0.26 7/0.10 11/0.08 14/0.07 19/0.06 28 0.081 1/0.32 7/0.12 11/0.10 16/0.08 21/0.07 28/0.06 26 0.129 1/0.40 7/0.16 9/0.14 11/0.12 16/0.10 25/0.08 33/0.07 45/0.06 24 0.205 1/0.50 7/0.20 14/0.14 19/0.12 26/0.10 41/0.08 53/0.07 73/0.06 22 0.326 1/0.65 7/0.26 11/0.203 13/0.18 17/0.16 22/0.14 29/0.12 42/0.10 65/0.08 20 0.518 1/0.80 7/0.30 10/0.26 12/0.23 16/0.203 20/0.18 26/0.16 34/0.14 46/0.12 66/0.10 18 0.823 1/1.02 7/0.40 10/0.32 16/0.26 20/0.23 26/0.203 33/0.18 41/0.16 54/0.14 73/0.12 65/0.127 104/0.10 16 1.309 1/1.29 7/0.50 11/0.40 17/0.32 25/0.26 32/0.23 41/0.203 52/0.18 65/0.16 85/0.14 119/0.12 165/0.10 14 2.081 1/1.63 11/0.50 17/0.40 26/0.32 40/0.26 50/0.23 65/0.203 82/0.18 103/0.16 135/0.14 183/0.12 264/0.10 12 3.309 1/2.05 17/0.50 27/0.40 41/0.32 54/0.28 80/0.23 102/0.203 130/0.18 164/0.16 10 5.261 1/2.60 27/0.50 42/0.40 65/0.32 99/0.26 126/0.23 162/0.203 206/0.18 261/0.16 8 8.366 1/3.26 26/0.65 67/0.40 104/0.32 157/0.26 6 13.30 1/4.12 27/0.80 40/0.65 68/0.50 105/0.40 165/0.32 4 21.1 5 1/5.20 26/1.02 42/0.80 64/0.65 107/0.50 168/0.40 2 33.6 3 1/6.54 4 26/1.29 42/1.02 67/0.80 101/0.6 5 171/0.50 0 53.48 1/8.254 26/1.63 41/1.29 66/1.02 106/0.80 161/0.65 1. 基准线规直径：直径5 mil（0.005 inch）为36 AWG： 2. 相邻线号之间以几何级数计算：见右框图中公式。例如：d18 = d36 × r (36-18) = 5 × 8.06053 = 40.3mils = 1.024mm d n = d 36× r (36 - n)( mil ) = 0.127 r(36 - n)( mm ) 其中，r = (460/5) 1/39 = 1.1229322

男女鞋尺码标准对照表

男鞋尺码标准对照表：（日本的单位为cm）欧洲（EUROPE）39 40 40.5 41 42 42.5 43 44 44.5 45 美国（US）6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 英国（UK）6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 日本（JAPAN）24.5 25 25.5 26 26.5 27 27.5 28 28.5 29 台湾（TAIWAN）69 70 71 72 73 74 75 76 77 78 中国码39 39.5 40 41 42 42.5 43 43.5 44 45 女鞋尺码标准对照表：（日本的单位为cm）欧洲(EUROPE）34 34.5 35 35.5 36 36.5 37 37.5 38 38.5 39 39.5 40 美国（US）4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 英国（UK）2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 日本（JAPAN）21 21.5 22 22.5 23 23.5 24 24.5 25 25.5 26 26.5 27 台湾（TAIWAN）64 65 66 67 68 69 70 71 72 73 74 75 76 中国码34 35 36 37 37.5 38 39 39.5 国际标准 ISO标准ISO 9407推荐的Mondopoint鞋码系统基于脚宽和平均脚长，以厘米为基本单位。各国、各地的鞋码英国码、美国码、日本码等。其中所谓的欧洲码欧洲码法国、德国等欧洲大陆国家的鞋码一般如下计算，单位是厘米：鞋码= 1.5*鞋楦长= 1.5*脚长+ 2 但具体大小可能因为鞋楦性状不同而有少量出入。美国、加拿大码美国、加拿大的鞋码是以用英寸衡量鞋楦长度：男鞋码= 3*鞋楦长-22 女鞋码(常见) = 3*鞋楦长-20.5 另外，还有一种比较少见的女鞋码，由美国鞋业协会(Footwear Industries of America)提出：女鞋码(FIA)=3*鞋楦长度-21

各国不锈钢牌号对照表

中国日本美国英国德国法国前苏联GB1220-92[84]JIS AISI BS 970 Part4DIN 17440NFA35-572TOCT5632 GB3220-92[84]UNS BS 1449 Part2DIN 17224NFA35-576~582 NFA35-584 1Cr17Mn6Ni5N SUS201201-------- 1Cr18Mn8Ni5N SUS202202------12×17.T9AH4 ----S2*******S16------ 2Cr13Mn9Ni4------------ 1Cr17Ni7SUS301301-------- ----S3*******S21X12CrNi177Z12CN17.07-- 1Cr17Ni8SUS301J1----X12CrNi177---- 1Cr18Ni9SUS302302302S25X12CrNi188Z10CN18.0912×18H9 1Cr18Ni9Si3SUS302B302B-------- Y1Cr18Ni9SUS303303303S21X12CrNiS188Z10CNF18.09-- Y1Cr18Ni9Se SUS303Se303Se303S41------ 0Cr18Ni9SUS304304304S15X2CrNi89Z6CN18.0908×18B10 00Cr19Ni10SUS304L304L304S12X2CrNi189Z2CN18.0903×18H11 0Cr19Ni9N SUS304N1304N----Z5CN18.09A2-- 00Cr19Ni10NbN SUS304N XM21-------- 00Cr18Ni10N SUS304LN----X2CrNiN1810Z2CN18.10N 1Cr18Ni12SUS305S30500305S19X5CrNi1911Z8CN18.1212×18H12T [0Cr20Ni10]SUS308308-------- 0Cr23Ni13SUS309S309S-------- 0Cr25Ni20SUS310S310S-------- 0Cr17Ni12Mo2N SUS315N316N,S31651-------- 0Cr17Ni12Mo2SUS316316316S16X5CrNiMo1812Z6CND17.1208×17H12M2T 00Cr17Ni14Mo2SUS316L316L316S12X2CrNiMo1812Z2CND17.1203×17H12M2 0Cr17Ni12Mo2N SUS316N316N-------- 00Cr17Ni13Mo2N SUS316LN----X2CrNiMoN1812Z2CND17.12N-- 0Cr18Ni12Mo2Ti----320S17X10CrNiMo1810Z6CND17.12-- 0Cr18Ni14Mo2Cu2SUS316J1---------- 00Cr18Ni14Mo2Cu2SUS316J1L---------- 0Cr18Ni12Mo3Ti------------ 1Cr18Ni12Mo3Ti------------ 0Cr19Ni13Mo3SUS317317317S16----08X17H15M3T 00Cr19Ni13Mo3SUS317L317L317S12X2CrNiMo1816--03X16H15M3 0Cr18Ni16Mo5SUS317J1---------- 0Cr18Ni11Ti SUS321321--X10CrNiTi189Z6CNT18.1008X18H10T 1Cr18Ni9Ti----------12X18H20T 0Cr18Ni11Nb SUS347347347S17X10CrNiNb189Z6CNNb18.1008X18H12B 0Cr18Ni13Si4SUSXM15J1XM15-------- 0Cr18Ni9Cu3SUSXM7XM7----Z6CNU18.10-- 1Cr18Mn10NiMo3N------------ 1Cr18Ni12Mo2Ti----320S17X10CrNiMoTi181 Z8CND17.12-- 00Cr18Ni5Mo3Si2--S31500--3RE60(瑞典)----0Cr26Ni5Mo2SUS329J1----------1Cr18Ni11Si4AlTi------------1Cr21Ni5Ti------------ 世界各国不锈钢标准钢号对照表

Gauge 板材换算

Gauge 板材換算

钢材理论重量计算钢材理论重量计算的计量单位为公斤（kg ）。其基本公式为：钢的密度为：7.85g/cm3 ，各种钢材理论重量计算公式如下：圆钢盘条（kg/m）W= 0.006165 ×d×d d = 直径mm 直径100 mm 的圆钢，求每m 重量。每m 重量= 0.006165 ×1002=61.65kg 螺纹钢（kg/m）W= 0.00617 ×d×d d= 断面直径mm 断面直径为12 mm 的螺纹钢，求每m 重量。每m 重量=0.00617 ×12 2=0.89kg 等边角钢（kg/m）= 0.00785 ×[d （2b – d ）+0.215 （R2 –2r 2 ）] b= 边宽 d= 边厚R= 内弧半径r= 端弧半径求20 mm ×4mm 等边角钢的每m 重量。从冶金产品目录中查出4mm ×20 mm 等边角钢的R 为3.5 ，r 为1.2 ，则每m 重量= 0.00785 ×[4 ×（2 ×20 – 4 ）+0.215 ×（3.52 – 2 ×1.2 2 ）]=1.15kg 不等边角钢（kg/m）W= 0.00785 ×[d （B+b –d ）+0.215 （R2 – 2 r 2 ）] B= 长边宽 b= 短边宽d= 边厚R= 内弧半径r= 端弧半径求30 mm ×20mm ×4mm 不等边角钢的每m 重量。从冶金产品目录中查出30 ×20 ×4 不等边角钢的R 为3.5 ，r 为1.2 ，则每m 重量= 0.00785 ×[4 ×（30+20 –4 ）+0.215 ×（3.52 –2 ×1.2 2 ）]=1.46kg 钢板（kg/m2）W= 7.85 ×d d= 厚厚度4mm 的钢板，求每m2 重量。每m2 重量=7.85 ×4=31.4kg 钢管（包括无缝钢管及焊接钢管（kg/m）W= 0.02466 ×S （D –S ）D= 外径 S= 壁厚外径为60 mm 壁厚4mm 的无缝钢管，求每m 重量。每m 重量= 0.02466 ×4 ×（60 –4 ）=5.52kg

文档之家

Gauge (non-)invariant Green functions of Dirac fermions coupled to gauge fields

中外鞋码对照表

各国钢号对照表

各种单位换算及公式

世界钢号对照表

各国尺码对照表

尺码对照表~衣服、裤子、鞋大小尺寸

压力单位换算方法

AWG-标准线径对照表

美国-中国-国际鞋码对照表

各种单位换算及公式

常用线规号码与线径对照表

线材线号AWG与导线截面积对照表 芯线

男女鞋尺码标准对照表

各国不锈钢牌号对照表

Gauge 板材 换算

常用线规号码与线径对照表[1]

线材线号AWG与导线截面积对照表芯线

Gauge 板材换算