On the Problems with Background Independence in String Theory

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IASSNS-HEP-93/66On the Problems with Background Independence in String Theory Samson L.Shatashvili ?#School of Natural Sciences Institute for Advanced Study Olden Lane Princeton,NJ 08540Dedicated to my teacher L.D.Faddeev on the occasion of his 60th birthday The problems with background independence are discussed in the example of open string theory.Based on the recent proposal by Witten I calculate the String Field Theory

action in conformal perturbation theory to second order and demonstrate that the proper treatment of contact terms leads to nontrivial equations of motion.I conjecture the form of the ?eld theory action to all orders.

October,93

In contrast with di?cult problems in realistic4d Field Theory models,where the theory is de?ned and an explicit analytic solution is not yet known,String Theory isn’t yet even de?ned.In many cases what we have is just a number of S-matrices for the processes when the background is?xed by our choice of conformal?eld theory in the?rst quantized formulation for amplitudes.Satisfactory formulation of String Theory would have been a formulation where we don’t need to refer to any particular classical background and these ”classical backgrounds”are given by solutions of some equations.The latter statement is very vague,because unfortunately it is not even clear(at least to the author)what should be the right terminology to address the question.It is believed,by analogy with the second quantized description of ordinary quantum?eld theory,that the understanding of vacuum structure of string theory as well as the nonperturbative character,can be achieved by developing the?eld theory language to describe the target space theory.It might well be that the procedure that allows us to construct second quantized?eld theory from Feynman sum over trajectories directly applied to string theory is not the best way to approach the problem and some other new ideas should be introduced.One of the most important ingredients of any construction has to be a background independence.

In this paper I will address the question of background independent formulation of string theory in the example of open string theory recently suggested by Witten[1]1.I can’t claim that at present every point is understood for the case of open string;this paper should be considered as an attempt to single out main problems and?nd a correct language based on this experience.The calculations and observations presented in section 2,together with?nal result(see below)might serve as a proper guide.This explains the title.

I’ll show that the integrals of total derivatives do not decouple inside the correlation functions that de?nes the String Field Theory action in the formalism of[1]due to contact term contributions.I’ll explain that these contributions have universal character and can’t be removed by change of renormalization scheme(this statement has the same origin as the one for gauge anomalies in?eld theory).This fact leads to slight modi?cations of the assumptions made in original paper[1]and also in[3].It was shown in[3]that under the key assumption of decoupling of total derivatives,plus the requirement that BRST operator on the boundary is coupling constant independent,theory has a linear character.

I’ll demonstrate here that including the contribution of total derivatives one also has to properly de?ne”BRST”operator on the boundary,which now necessarily should depend on couplings to satisfy the consistency condition.I’ll discuss the ambiguities related to this issue and will make a particular choice.In this setup I’ll calculate the?eld theory action in the lines of[3]using the conformal perturbation theory around some?xed point and demonstrate the existence of following relation:

?

S=?βi

2The fact that the string?eld theory action on the classical equations of motion is given by the world-sheet bosonic partition function was previously suspected in[5][6]

form.As a result this formalism doesn’t avoid the usual technical di?culties that are present in any other formulation of string?eld theory,although it is formally background independent and contains all string modes.

1.Boundary Problem and Open String Field Theory

In the beginning of this section we?rst will describe the construction of[1]with the emphasis of places where some assumptions are made.The idea of the construction in [1]is based on BV formalism.Let M be a supermanifold which is equipped with closed, nondegenerate odd simplectic structureωand U(1)symmetry,called ghost number U.This means that in Darboux coordinatesψ,θon M withψfermionic andθbosonicω=dψdθandωhas ghost number1.In analogy with ordinary(bosonic)simplectic manifolds one can de?ne the Poisson Brackets,antibracket,with

{A,B}=?r A

?t j

.(1.1)

One can show that the following two simple facts take place:

i.If V is a vector?eld that generates the symmetries ofω,which means that(di V+ i V d)ω=0,then there exists a function S that

dS=i Vω.(1.2)

ii.Vector?eld de?ned by(1.2)generates a symmetry ofωfor any function S.

From the above immediately follows that the Poisson brackets of function S,{S,S}, de?ned by(1.2)is annihilated by d and thus the function{S,S}is a constant

d{S,S}=0.(1.3) The equation

{S,S}=0(1.4)

is called the BV master equation and S is the action functional if it solves the master equation.Every solution of(1.4)is automatically gauge invariant[1],[7].;the variation of the action under any symplectic transformation

δt i={t i,K},(1.5)

generated by hamiltonian function K(odd function),is given byδS={S,K}and for {S,K}=0,it vanishes;trivial transformations are given with K={S,Λ}.

In the quantization of gauge theories the action S is given on subspace of M with U=0,S0,and we have to?nd S.That is in fact what the Faddeev-Popov procedure does in the case of Gauge Theories.In the case of String Field Theory,the idea of[1]was to identify the antibracket and vector?eld in terms of the world-sheet theory and thus identify S as the action of the corresponding target space theory.It was claimed in[1] that this can be done in the case of Open String in a background independent way.The following identi?cations were proposed:

ω:ω(δO,δO)= ?Σdσ1 ?Σdσ2<δO(σ1)δO(σ2)>(1.6)

V:δV O={Q,O}(1.7) where<...>formally is de?ned through the world-sheet theory given by path integral corresponding to the2d action

L a= Σd2z(12πb ij D i c j)+ ?ΣdθV(X,b,c,t)(1.8) Here,the?rst term is the closed string background and the second term describes an arbitrary boundary interaction,parametrised by coupling constants t i(in general there are in?nite number of coupling constants),with the condition that the boundary operator V has the form

V=b?1O,(1.9) with O being a general operator of ghost number1.Q is a BRST operator de?ned by BRST current:Q= C dσJ BRST with contour C approaching the boundary?Σ3and b?1= C b(v),b(v)=v i b ij?i k dx k with v i being the killing vector that generates the rotation of disc.This world-sheet action is also equipped with an ultraviolet cuto?a.

From the above identi?cations we have the de?nition of string?eld theory action:

1

dS=

3We will not worry about generality and assume thatΣis just a disc.

where d=dt i d/dt i and<...>again denotes un-normalized correlation function.Witten has shown that(1.6)gives a closed form and it is invariant under(1.7).We need for future use to repeat his arguments and stress the points where some assumptions are made.4 The fact thatωde?ned by(1.6)is closed follows from the identity:

0=(1.11)

Here we use the de?nition of b?1and take two limits:?rst we shrink the contour C to a point and get zero;second we take the limit when the contour approaches the boundary ?Σand get the right hand side in(1.11).Thus,in the notationδi O=?

ω(δi O,δj O)?

?t k

(1.12)

?cyclic permutations=<(b?1δk O)δi Oδj O>?cyclic perm.=0

and the last step follows from(1.11).

BRST invariance of(1.6)is equivalent to exactness of the right hand side in(1.10). This follows from the simple observation that because the transformation law ofωis ω′=ω+?(i V d+di V)ωand we already have shown that dω=0,what we have to show is that di Vω=0.We have

d=<(b?1dO)dO{Q,O}>?

.(1.13)

??

If we use the identity(1.11)for the?rst term in(1.13)and the de?nition(1.9)we get:

<(b?1dO)dO{Q,O}>?+

(1.14)

+<(dO)2[L0,O]>?<(dO)2[Q,V]>=0.

We are considering a deformation of the critical string,so we can drop all terms of the type<{Q,...}>0,where subscript0means the expectation value in the unperturbed theory of some number of operators,using the argument of the contour deformation in the de?nition for Q,and thus in the last term of(1.14)we can integrate by parts in the path

integral to obtain+<{Q,(dO)2}>;the same is true for the last term in(1.13),which leads to+1

<(dO)2[L0,O]>=0(1.15)

2

and we see thatω,de?ned by(1.6)is BRST invariant only if the right hand side in the equation(1.15)is identically zero.

It was concluded in[1]that(1.6)is BRST invariant because of the following two assumptions:

?Q

O(θ)dθ=0(1.17)

?θ

here,in(1.17),the?rst identity means that L0is a generator of the rotation of circle, and the second identity assumes that total derivatives decouple inside the correlation functions.5

Comment:the second correlator in(1.15),the one with total derivative inside the integral,generically is not zero and might receive the contribution from the boundary of moduli space(position of operators on the circle are moduli).Thus,we have to treat such terms and include their contribution.Or,if we want to set up such a scheme during the evaluation of correlation functions in(1.10),when(1.16)is satis?ed once inside the correlator,we have to make sure that our regularization scheme leads to decoupling of total derivatives in the second term in(1.15).The latter is a nontrivial statement and in the next section we are going to address this question in detail.The identity in(1.15)should be considered as the requirement for operator Q;so,Q,when the contour approaches the boundary?Σshould depend on the couplings according to equation(1.15)and this leads to consistency condition on the construction.From the point of view of conformal perturbation theory the above requirement means that we have to use the parallel transport of Q,consistent with(1.15)when we move away from the critical point t CF T.It happens that only the P SL(2,R)subalgebra of Virasoro algebra is relevant,thus what one needs is to deform this subalgebra by including the contributions of boundary term.In the

next section we will evaluate the right hand side in(1.10)and formulate this consistency

condition in more clear terms for the case when the boundary interaction doesn’t mixes

ghosts and matter.

At the end of this section as an illustration I would like to discuss a known example of

perturbation of a conformal?eld theory(closed string)by dimension one operator,where

the decoupling of total derivatives doesn’t takes place and the obstruction is aβ-function

[10].Similar calculations will be performed in the next section for open strings.

Consider some CFT perturbed by a dimension one operator V i t i.6We will denote

the correlation functions in the perturbed theory by<<...>>and those in the unper-

turbed theory by<..>;so,the partition function for can be written as<<1>>,or

.One can calculate the trace of stress-tensor in the perturbed theory in the following way.We start from the expectation value of the holomorphic part of stress

tensor<>and use the operator expansion algebra

T(z,ˉz)V i(w)=

1

z?w

?

?w

(

1

?w i

(

1

(n?1)!

( V)n?1>.(1.19)

If we claim that the contribution of the total derivative in the right hand side is zero,we will conclude that the expectation values of stress tensor is zero;but the latter is wrong–we know that the following relation holds:

?

?z <>=βi

?

6I would like to thank A.Polyakov for pointing out to me the following example.

V i (w 1,ˉw 1)V j (w 2,ˉw 2)=g ij

|w 1?w 2|2V k (w 2)+...

(1.21)Now we see that because of the poles in (1.19)and (1.21),there is nonzero boundary contribution in the integral over w i in (1.19).For this we substitute (1.21)in (1.19).After integration over w i in (1.19)we are left with the boundary contour integral,with small contour surrounding each point w j ;denoting w i =w j +ρe iθwith small ρ,we get:

<>= ij t i t j < d 2

w j dθρe ?iθ1ρ4+

+C k

ij (n ?2)!( V )n ?2>.

(1.22)If we expand the denominator in (1.22)in the powers of ρand integrate over θ,we see that only second term contributes,with ?nal answer:

<>=C k ij t i t j d 2w 1

conformal?eld theory with stress tensor T and corresponding BRST operator Q.When the contour C approaches the boundary of the disc the operator

Q= dθc(θ)[T m+1

2 2π

dθ1dθ3<

3

c(θ3)V(θ3)>>

+

1

2 2π

dθ1dθ2(2cos(θ1?θ2)?2)<>=

= dθ1dθ2cos(θ1?θ2)<>?d<< dθV(θ)>>+d<<1>>.(2.4) If we use the notation L n= 2π0dθe inθT m(θ),the second term in(2.2)can be written as a combination of three expressions:

1

<< dθ1e iθ1dV(θ1)[L?1, dθ2V(θ2)]>>=

=< dθe iθdV(θ)[L?1,exp(iL int)]>,(2.6) << dθ1dV(θ1)[L?1, dθ2e iθ2V(θ2)]>>=

=.(2.7) We need two more identities:

=d<<[L?1, dθe iθV(θ)]>>?

?<<[L?1, dθe iθdV(θ)]>>?<<[dL?1, dθe iθV(θ)]>>,(2.8) and?nally for the second term in(2.8)

<<[L?1, dθe iθdV(θ)]>>=

=?<[L?1,exp(iL int)] dθe iθdV(θ)>+<[L?1,exp(iL int)] dθe iθdV(θ)]>.(2.9) Here we used the notation where L int is the boundary interaction term,and dL?1= dt i?

dS =d i

?θ2sin (θ1?θ2)<>?? dθ1dθ2sin (θ1?θ2)<

(<<[dL ?1, dθe iθV (θ)]>>?c.c.).

(2.12)

Now I would like to require that under proper de?nition of renormalization scheme and the generators of SL (2,R )subalgebra,the object X is identically zero.One should note that the consistency condition (1.15)requires that X is just an exact form,thus there is an ambiguity in the de?nition of Q and equivalently the symmetries of (1.6).Moreover it is not guaranteed that in the deformed theory the stress tensor,that enters in the de?nition of Q ,is deformed accordingly to this requirement.Below I will give arguments that it is indeed the case and that the vanishing of X is a natural choice.They couldn’t be considered as a rigorous proof to all orders in t ;they are just arguments and most likely they can lead to such a proof.Before I turn to this very important question let us evaluate the ?rst term in (2.12),to be sure that the total derivative doesn’t make it zero.We have in the lowest order in t :

dθ1dθ2?sin 1

|sin 1

the”resonance term”,is convergent in the limit when we remove the cuto?,and others diverge.These divergent terms can be removed by rede?nition of couplings or the same, by a subtraction procedure(see below),while the constant term is universal and can’t be removed.Also,there should be a higher order correction in couplings in(2.13).

We see that,like in the example for closed string at the end of the previous section, total derivative in X doesn’t decouple and is proportional toβ-function coe?cient C k ij; thus(1.17)fails,so does(1.16).

Until now we had avoided the question about the transformation properties of bound-ary operator.To proceed further it is necessary to know the action of L?1,L0and L1on V’s.What we need to cancel the contribution of(2.13)in X is:

?

?t i =δj i?i+4c j

ik

t k+....,(2.18)

andβj is theβ-function for operator V j.This deformation is a very natural one.7In fact what we need is(2.17)in the?rst nontrivial order in couplings to compare with(2.13), because the latter we are able to calculate only up to this order.Here are the arguments in support of(2.17):consider the auotomorphizms of disc:

z′=α

z?z0

7There are similarities between(2.17)and the boundary problem analog of anomaly equation (1.20),recently derived by Zamolodchikov[12],see also[13].I would like to thank A.Zamolod-chikov for sharing his insight on the problem of boundary deformations with me.

with|z0|<1and|α|=1.The requirement,that corresponding P SL(2,R)subalgebra of Virasoro algebra is not broken in perturbed theory,?xes the transformation law(2.17).In the case of closed string,the transformation properties under constant shift is standard, and under dilatation is controlled by the Callan-Symanzik equation,that leads to change of classical dimension to anomalous dimension[8];so these two elements are universal,and the third one is?xed by the requirement,mentioned above.The open string version is given by(2.17)and leads to(2.16).We see from this expression that they are compatible in the lowest order in couplings and guarantee that X vanishes.What is needed to complete the proof is that one has to show the compatibility of(2.17),in particular regularization scheme (note that higher order terms inβ-function are scheme dependent),with the vanishing of X in(2.12)and(2.13)to all orders..

Thus,the?rst term in equation(2.11)de?nes the string?eld theory action

i

S=

Z(t)+Z(t).(2.22)

?t i

If we remember that structure constants in(2.13)were cuto?dependent and this depen-dence we removed by a subtraction,we might have kept it up to(2.22).The reason is

that as it follows form Poincare-Dulac Theorem8about vector?elds,every vector?eld can be linearized by appropriate rede?nition of coordinates up to the resonant terms,and the resonant condition is related to the zero modes of linear partα1,...,αn.The N-th order term can not be removed by this rede?nition if and only if there exists the integer relation of the form:

αs= N1m iαi(2.23) with(m1,...)integers and m k≥0, m k≥2and(2.23)is called the resonance relation. The linear term forβi is given by(1??i)t i,thus the resonance condition in the second order is the one we had written before(2.15):1??k=1??i+1??j.They correspond to?nite terms in(2.13)and can’t be removed by coordinate transformation.This in fact proves that the non-vanishing of total derivative term in S is universal.

The expression(2.22)shows that for exactly marginal deformations of base point (which is a particular CFT)action S is the same as partition function and this con?rms the statement of[4].Obviously,assuming thatβ=0(?i=1and c k ij=0in the perturbation theory)from the begining and going through our calculations again we get dS=0.Because any attempt to calculate string?eld theory action in the present approach should use the perturbation theory we can’t make any statement about global properties of action. Also,it is di?cult to check above statement about equation of motion directly from?nal expression(2.22)without going to world-sheet and using the identities described in this Section;it would be very interesting to?nd such https://www.doczj.com/doc/889868744.html,st important comment related to these questions:we couldn’t compare two actions(note that dependance on t’s enter throughβ)if they are calculated in perturbation theory arround di?erent points in space of t’s.For this we will need the natural paralel transport in the space of theories that we unfortunately don’t have;we only know the deformed relations for SL(2,R)generators in perturbation theory.Thus,the result is not truly background independent even it looks so formally.

Acknowledgments:I would like to thank A.Zamolodchikov,E.Verlinde and E.Witten for very useful discussions.

References

[1] E.Witten,Phys.Rev.,D46(1992)5446,hep-th-9208027.

[2] A.Sen,B.Zwiebach,Quantum Background Independence of Closed String Theory,

Preprint MIT-CTP-2244,TIFR-TH-93-37,hep-th/9311009.

[3]S.Shatashvili,Phys.Lett.B311(1993)83,hep-th-9303143.

[4] E.Witten,Phys.Rev.,D47(1993)3405,hep-th-9210065.

[5] E.Fradkin and A.Tseytlin,Phys.Lett.B163(1985)123.

[6] A.Abouelsaood,C.Callan,C.Nappi and S.Yost,Nucl.Phys.B280(1987)559.

[7] A.Sen and B.Zwiebach,A note on gauge transformations in Batalin-Vilkovisky the-

ory,Preprint MIT-CTP2240,TIFR-TH-93-38,hep-th/93099027.

[8] A.B.Zamolodchikov,Yad.Fiz.46(1987)1819,Sov.J.Nucl.Phys.46(1987)1091.

[9]K.K.Li and E.Witten,Phys.Rev.D,48(1993)853,hep-th-9303067.

[10] A.Polyakov,Unpublished,A.M.Polyakov,Gauge Fields and Strings,Harwood,1991.

[11]K.Ranganathan,H.Sonoda,B.Zwiebach,Connection on the state space over Con-

formal Field Theories,Preprint MIT-CTP-2206,hep-th-9304053.

[12] A.Zamolodchikov,Unpublished

[13]S.Ghoshal and A.Zamolodchikov,Boundary S-matrix and boundary state in two-

dimensional integrable quantum?eld theory,Rutgers Preprint RU-93-20,hep-th-9306002.

[14] A.Zamolodchikov,Adv.St.in Pure Math.,19(1989)641.

(完整版)小学英语总复习--常用介词介绍及专项练习

小学英语总复习 小学英语介词总结 介词（Preposition） 一、概述 介词是英语中很活跃的词，一般置于名词之前。它常和名词或名词性词语构成介词短语。同一个介词常和不同的词语搭配形成固定搭配，表示不同意义。 二、常用介词的基本用法 at ①表示时间：I go to school at seven every day 我每天早上7点去上学。 ②表示在某一具体地点：He is standing at the bus stop 他站在公共汽车站。 ③表示动作的方向、目标：Let me have a look at the picture 让我看看这幅图。 ④用于某些固定搭配：at once 立刻、马上at last 最后 at the same time 同时at first 开始时 not at all 一点也不 about ①表示大约时间：It’s about six o'clock now. 现在大约6点钟了。 ②表示地点；在……周围：Everything about me is so beautiful 我周围的一切都那么美好。 ③关于，对于：We are talking about the news. 我们正在谈论新闻。 after ①在……之后：After dinner I watch TV. 晚饭后我看电视。 ②在……后面：He came into the room after me. 他在我后面进了房间。 behind ①在……之后：There is a bike behind the tree. 树后有一辆自行车 ②比……晚，迟于：The train is behind time. 火车晚点了 by ①在……旁：He is sitting by the bed. 他正坐在床边。 ②到……时候：We have learned three English songs by now. 到现在为止，我们已经学会了三首英文歌曲。 ③以……方式：I go to school by bus. 我乘公共汽车去上学。 ④用于某些固定搭配：one by one 一个接一个by the way 顺便说一句

小学常用介词的基本用法

常用介词的基本用法 at ①表示时间：I go to school at seven every day 我每天早上7点去上学。 ②表示在某一具体地点：He is standing at the bus stop 他站在公共汽车站。 ③表示动作的方向、目标：Let me have a look at the picture 让我看看这幅图。 ④用于某些固定搭配：at once 立刻、马上at last 最后 at the same time 同时at first 开始时 not at all 一点也不 about ①表示大约时间：I's about six o'clock now. 现在大约6点钟了。 ②表示地点；在……周围：Everthing about me is so beautiful 我周围的一切都那么美好。 ③关于，对于：We are talking about the news. 我们正在谈论新闻。 after ①在……之后：After dinner I watch TV. 晚饭后我看电视。 ②在……后面：He came into the room after me. 他在我后面进了房间。 behind ①在……之后：There is a bike behind the tree. 树后有一辆自行车 ②比……晚，迟于：The train is behind time. 火车晚点了 by ①在……旁：He is sitting by the bed. 他正坐在床边。 ②到……时候：We have learned three English songs by now. 到现在为止，我们已经学会了三首英文歌曲。 ③以……方式：I go to school by bus. 我乘公共汽车去上学。 ④用于某些固定搭配：one by one 一个接一个by the way 顺便说一句 for ①为，给，替：I'll make a card for my teacher. 我要给老师做卡片。 ②由于：Thank you for helping me. 你帮我。 ③表示给（某人）用的：There is letter for you. 这儿有你一封信。 in ①在……里面：The pencil is in the desk. 铅笔在课桌里。 ②在一段时间里：We have four classes in the morning. 我们上午有四节课。 ③用，以：What's this in English? 这用英语怎么说？ ④在某一年份，季节，月份：in 2002, in spring, in January ⑤表示状态，服饰：Helen is in yellow. 海伦身穿黄色衣服。

小学常用介词练习

小学常用介词练习 ( )1.___ the afternoon of May, we visited the old man. A. On B. At C. In ( )2.Many people work ___ the day and sleep ___ night. A. on at B. in in C. in at ( )3.He speaks Japanese best ____ the boy students. A. between B. with C. among ( )4.A wolf ___ a sheep skin is our dangerous enemy. A. with B. in C. on ( )5.Joan hopes to come back ___ three days. A. after B. for C. in ( )6.They sent the letter to me ___ mistake. A. by B. for C. with ( )7.He left home ___ a cold winter evening. A. at B. on C. in ( )8.Shanghai is ____ the east of China. A. in B. on C. to ( )9.____ my father’s help, I have finished my composition. A. Under B. On C. with ( )10.He’s very strict ____ himself and he’s very strict ___ his work. A. with in B. in with C. with with ( )11.I really can’t agree ____ you. A. to B. on C. with ( )12.The shop won’t open ___ nine in the morning. A. until B. at C. during ( )13.How about ___ the flowers now? A. watering B. are watering C. watered ( )14.She spent all his money ___ books. A. in B. with C. on ( )15.They are talking ___ low voices. A. with B. in C. on ( )16.It’s very kind ___ you to help us. A. for B. to C. of ( )17.What will you have ___ breakfast this morning? A. with B. for C. by ( )18.A plane is flying ____ the city. A. on B. over C. above ( )19.You are free to speak ___ the meeting. A. at B. in C. on ( )20.Mr. Green will stay in China___ Friday. A. to B. on C. till ( )21.It’s wrong to play jokes ___ other people. A. on B. of C. with ( )22.Which color do you like? I prefer blue ___ red. A. for B. as C. to ( )23.The student will give us a talk ___ how to use our spare time. A. for B. on C. in ( )24.I paid two hundred yuan ___ that kind of bicycle.

小学常用介词练习(附答案)

常用介词练习 ( ) the afternoon of May, we visited the old man. A. On B. At C. In ( ) people work ___ the day and sleep ___ night. A. on ; at B. in ; in C. in ; at ( ) speaks Japanese best ____ the boy students. A. between B. with C. among ( ) wolf ___ a sheep skin is our dangerous enemy. A. with B. in C. on ( ) hopes to come back ___ three days. A. after B. for C. in ( ) sent the letter to me ___ mistake. A. by B. for C. with ( ) left home ___ a cold winter evening. A. at B. on C. in ( ) is ____ the east of China. A. in B. on C. to ( ) my father’s help, I have finished my composition. A. Under B. On C. with ( )’s very strict ____ himself and he’s very strict ___ his work. A. with ; in B. in ; with C. with ; with ( ) really can’t agree ____ you.

小学生常见介词

?小学常见介词： 1.on (1) 在------上面The book is on the desk. (2) 在------（哪一天/星期）What do you do on Wednesday? (3) 在------（月、日）My birthday is on August 2nd. 2. in （1）在------里面The pens are in the pencil-box. (2)在------（哪一年/月）His birthday is in October. He worked here in 1992. (3 ) 在------（地方）He works in Dongguan. (4 ) 在------之内What are you going to do in 20 years? (5 ) 在------（早上、下午、晚上） I do morning exercises in the morning every day. I usually play basketball in the afternoon. I often do my homework in the evening. 3. under 在------底下There is a ball under the bed. 4. near

在------附近There is a book shop near our school. 5. in front of 在------前面 A boy is standing in front of the house. 6. beside 在------旁边 A football is beside the door. 7. next to 紧挨着There is a bus station next to No. 13 Middle School. 8. over 在------正上方A bridge is over the river. 9. on the left 在------左边The bookstore is on the left. 10. on the right 在------右边The hospital is on the right. 11. before 在……之前Mike sits before me. 12. after 在------以后He went home after school. 13. in the middle

小学介词常用示例

小学介词常用示例 表示时间的介词称为时间介词.表示时间的介词有：at, on, in, before, after 等. 一、at, on和in ① at 表示：（在（某时刻、时间、阶段）,在……岁时） My cousin joined the army at fifteen. 我表哥十五岁参的军. ② on 表示：在（某日）,在周末,在……节日 He was born on the 15th of August in 1769. 他出生于1769年8月15日. ③ in 表示：在……事后,在……期间,在……年/月 She went to America in 2000. 她2000年去了美国. at, on 和in 作时间介词的比较： ① at 表示具体时间点. ② on 后可以跟表日期、星期、节日的词,还可以指具体某一天的早、中、晚. ③ in 泛指一天的早、中、晚,还可以表示一段时间,如：周、年、月、季节等. 二、before和after ① before 表示：在……之前 before eight o’ clock 八点之前 Spring comes before summer. 夏天之前是春天. ② after 表示：表示……之后 after lunch 午饭之后 Come to my office after school. 放学后请来我办公室. 表示做某事的方法、手段的介词有by, with, in, at, on. 一、by by表示：用,以,靠,通过……方式.by表示手段时后接动作或制作方式.“by + 交通工具”表示交通方式. by bike 骑车 by bus 坐公车 by taxi 搭出租 by train 坐火车 by ship 乘船 by air 坐飞机 Linda usually goes to work by subway. 琳达通常做地铁上班. She makes a living by teaching. 她考教书谋生. 二、with with 表示：用,以.with表示手段时,后接工具、材料或具体内容. write with a pen 用钢笔写 eat with knife and fork 用刀叉吃 see with one’s eyes 用眼睛看 I killed the fly with a swatter. 我用苍蝇拍打死那只苍蝇. She cut the cake with a knife. 她用刀切开了蛋糕.

小学英语常用介词用法

小学英语常用介词用法 摘要：英语介词并不很多，但其用法灵活多样。掌握常用介词的用法及常见的介词搭配，是学习英语的重点和难点。 关键词：英语介词用法 介词是英语中一个十分活跃的词类，在句子的构成中起着非常重要的作用。介词也是英语中的一个最少规则可循的词类，几乎每一个介词都可用来表达多种不同的含义；不同的介词往往又有十分相似的用法。因此，要学好介词，最好的方法就是在掌握常用介词的基本用法的基础上，通过广泛阅读去细心地揣摩，认真地比较，归纳不同的介词的用法，方能收到良好的效果。那么，什么是介词呢？小学常用的介词都有哪些以及它们的用法？ 一·介词 1 介词的含义 介词又叫前置词，是一种虚词，用来表明名词，代词（或相当于名词的其他词类，短语或从句）与句中其他词关系的词。介词不能重读，不能单独做句子成分，必须与它后面的名词或代词（或相当于名词的其他词类，短语或从句）构成介词短语，才能在句子中充当一个成分。介词后面的名词，代词或相当于名词的部分称为介词宾语，简称介宾。 2介词的分类 1）根据介词的构成形式，可将介词分为简单介词，合成介词，双重介词，短语介词四类。而小学英语中涉及到的介词仅为简单介词和一些短语介词，如：after（在……之后），against（反对），along（沿着），among（在……之中），at（在），behind（在……后面），near（在……附近），into（在……里），in（在……内，用，戴），from（从），for （为，给），except（除……之外），by（乘，在，由，到），on the left (在左边),on the right (在右边)······ 2）根据介词的意义，可将介词分为表示空间关系的介词，表示时间的介词，表示原因，目的的介词，表示手段的介词和其他介词。如：表示时间的介词in，on，at，表示方位的介词in，on，to······下文则主要是从介词的意义方面来讲介词的用法。 二·小学常用英语介词 1课文中常出现的介词 1）about（关于，大约）：a book about animals 一本关于动物的书。 2）above（在……上面）：a map above the blackboard 黑板上方的一张地图，above all 首要的是。 3）across（穿过，跨过）：a bridge across the river 跨过河的一座桥 4）after（在……之后）：after breakfast 早饭后，after school 放学后，after class 课后 5）against（反对）：play against them 跟他们比赛。 6）along（沿着）：plant trees along the lake 沿着湖边植树。 7）among（在……之中）：among the workers 在工人们中间，among the trees 在树丛中。 8）at（在）：at home在家，at school 在学校，at work 在工作。 9）before（在……之前）：before class 课前，before lunch 午饭前 10）behind（在……后面）：behind the house 在房子后面，behind the door 在门后。 11）near（在……附近）：near the river 在河边，stand near the door 站在门旁。 12）into（在……里）：come into the classroom 进入教室，fall into the water 掉进水里

(完整版)小学英语常用介词及用法

常见介词及用法 (一)表示时间的介词 1.英语里最常见的时间介词有：at, in, on, before, after和from。 2.at , in和on这三个词都表示时间。 ?at主要指具体的钟点：at half past eight 在八点半 ?in一般指某一段时间：in January 在一月份 ?on指具体在某一天：on Monday 在星期一 3.before和after表示时间的先后顺序。 ?before表示“在……之前”。 You should wash your hands before eating. 吃饭前你应该洗手。 ?after表示“在……之后”。 They often play basketball after dinner. 他们放学后经常打篮球。 4.from作时间介词含有“从……开始”的意思，常和to连用，组成 “from…to…”的结构，表示“从……到……”的意思。 We go to school from Monday to Friday. 我们从周一到周五上学。 (二)表示方位的介词，也就是表示位置和地点的介词。 1.小学阶段常见的方位介词有：on, in, at, under, over, above, below, about, around, between等。 2.on, over和above 这三个词都有“在……上面”的意思，但它们所表示的方位还是有些不同。 ?on表示两个物体的表面相互接触。如： There is a book on the desk. 桌上有一本书。 The boy is sleeping on the desk. 那个孩子睡在地上。 ?over表示“在……的正上方”,两个物体表面没有接触。如： There is a light bulb over my head. 在我头顶上有一个灯泡。 ?above表示两个物体中一个在另一个的上方，如： The plane is flying above the clouds. 飞机上云层上飞行。

小学常用介词的基本用法

常用介词的基本用法 1、at ①表示时间：I go to school at seven every day 我每天早上7点去上学。 ②表示在某一具体地点：He is standing at the bus stop 他站在公共汽车站。 ③表示动作的方向、目标：Let me have a look at the picture 让我看看这幅图。 ④用于某些固定搭配：at once 立刻、马上at last 最后 at the same time 同时at first 开始时 not at all 一点也不 ; 2、about ①表示大约时间：I's about six o'clock now. 现在大约6点钟了。 ②表示地点；在……周围：Everthing about me is so beautiful 我周围的一切都那么美好 ③关于，对于：We are talking about the news. 我们正在谈论新闻。 3、after ①在……之后：After dinner I watch TV. 晚饭后我看电视。 ②在……后面：He came into the room after me. 他在我后面进了房间。 4、behind ; ①在……之后：There is a bike behind the tree. 树后有一辆自行车 ②比……晚，迟于：The train is behind time. 火车晚点了 5、by ①在……旁：He is sitting by the bed. 他正坐在床边。 ②到……时候：We have learned three English songs by now. 到现在为止，我们已经学会了三首英文歌曲。 ③以……方式：I go to school by bus. 我乘公共汽车去上学。 ④用于某些固定搭配：one by one 一个接一个by the way 顺便说一句 6、for ] ①为，给，替：I'll make a card for my teacher. 我要给老师做张卡片。 ②由于：Thank you for helping me. 谢谢你帮我。 ③表示给（某人）用的：There is letter for you. 这儿有你一封信。 7、in ①在……里面：The pencil is in the desk. 铅笔在课桌里。 ②在一段时间里：We have four classes in the morning. 我们上午有四节课。 ③用，以：What's this in English 这用英语怎么说 ④在某一年份，季节，月份：in 2002, in spring, in January 【 ⑤表示状态，服饰：Helen is in yellow. 海伦身穿黄色衣服。 ⑥在……方面：He is weak in English. 他的英语不行。 ⑦用于某些固定搭配：in front of 在……前面 in the end 最后

小学生常见介词

小学常见介词: ⑴在-——上面The book is on the desk. (2) 在 --- (哪一天/ 星期)What do you do on Wedn esday (3) 在 --- (月、日) My birthday is on August 2nd. 2. in (1) 在--- 里面The pens are in the pen cil-box. ⑵在——(哪一年/ 月)His birthday is in October. He worked here in 1992. (3 ) 在----- (地方) He works in Don ggua n. (4 )在 ----- 之内What are you going to do in 20 years (5 ) 在------ (早上、下午、晚上) I do morning exercises in the morning every day. I usually play basketball in the afternoon. I ofte n do my homework in the eve ning. 3. un der

在-- 底下There is a ball under the bed. 4. near 在-- 附近There is a book shop near our school. 5. in front of 在-- 前面A boy is standing in front of the house. 6. beside 在-- 旁边A football is beside the door. 7. next to 紧挨着There is a bus station next to No. 13 Middle School. 8. over 在-- 正上方A bridge is over the river. 9. on the left 在-- 左边The bookstore is on the left. 10. on the right 在-- 右边The hospital is on the right. 11. before 在... 之前Mike sits before me. 12. after 以后He went home after school. 13. in the middle

小学常用介词 归纳

系表+介词 Be angry about /at/ with 对.....感到生气Be sorry about to 对.....感到抱歉Be pleased with /at...... 对.....感到高兴 Is famous as... 以.....身份/职业而闻名Is famous for... 以........而闻名 Be Interested in... 对.....感兴趣 Be poor / Weak in... 在......方面薄弱Be afraid of....... 害怕........ Be sure of 对........有把握 Be sure about对........有把握 Be polite to... 对........有礼貌 Be Friendly /kint to... 对.....友好 Be good for 对.....有益Be Strict in... 对......严格（对事）Be Strict with ....... 对..........严格（对人）Be Good at..... 擅长于....... Be surprised at... 对........感到惊讶 Get ready for... 为.........做好准备 Be rich in... 在.........方面富有 be different from...与..........不同 Be fond of 喜欢.......... Be proud of...... 为..........而自豪 Be rude to....... 对..........粗鲁 Be kind to.../be good with善待.......... Be busy with.......... 忙于.......... 介词+名词 At night 在夜间 at once 立刻 At home在家 After school 放学后 All in all / In general 总的来说 by the lake 在湖边 By oneself / alone 独自 for example 例如 At class 在上课 On time按时 To one's surprise 令某人惊讶的是On foot 步行 On business / A business travel出差 At noon 在中午at first当初、起先 At work 在上班 after all 毕竟 By the way 随便问一下 By the way 到现在为止 By day在白天 For fun / To make fun of 开玩笑地 In time 及时 In Surprise 惊讶地 In tinge及时 In town 在城里 By train / car / bu s 乘火车/小汽车/公交 名词+介词 .Answer (key) to ... .......的答案（钥匙）Note to.... .....注释 Visit to 对.........访问 Love for... 对.........的热爱Difficulty with .......的困难 Way to / The road to... 通向.........的道路question with ... / the question of............的问题Trouble with. ..........的麻烦 动词+介词 Worry about... 为.........而担忧 talk about 谈论 Speak about 谈论、谈到 Hear bout 听说 Laugh at 嘲笑 Shout at... 对.........吼叫 Look for 找 Ask for / Get request 要求得到 Hear from.. / Receive a letter from..收到.......来信Come from 来自 Listen to 听 Arrive at / in 到达Help oneself to 随便吃、随便用Think about考虑、认为Have a look /look at 看一看 Smile at... 对.........微笑Knock at the ...... 敲 Take care of /care for 照料 wait for等待 Learn from..... 向.........学习die from 死于 Arrive / get to 到达Write... To... 给.........写信Say hello to...... 向.........问好

(完整版)小学常用介词练习(附答案)

常用介词练习 ( )1.___ the afternoon of May, we visited the old man. A. On B. At C. In ( )2.Many people work ___ the day and sleep ___ night. A. on ; at B. in ; in C. in ; at ( )3.He speaks Japanese best ____ the boy students. A. between B. with C. among ( )4.A wolf ___ a sheep skin is our dangerous enemy. A. with B. in C. on ( )5.Joan hopes to come back ___ three days. A. after B. for C. in ( )6.They sent the letter to me ___ mistake. A. by B. for C. with ( )7.He left home ___ a cold winter evening. A. at B. on C. in ( )8.Shanghai is ____ the east of China. A. in B. on C. to ( )9.____ my father’s help, I hav e finished my composition. A. Under B. On C. with ( )10.He’s very strict ____ himself and he’s very strict ___ his work. A. with ; in B. in ; with C. with ; with

小学常用介词的基本用法

小学常用介词的基本 用法 -CAL-FENGHAI-(2020YEAR-YICAI)_JINGBIAN

常用介词的基本用法 1、at ①表示时间： I go to school at seven every day 我每天早上7点去上学。 ②表示在某一具体地点： He is standing at the bus stop 他站在公共汽车站。 ③表示动作的方向、目标： Let me have a look at the picture 让我看看这幅图。 ④用于某些固定搭配： at once 立刻、马上 at last 最后 at the same time 同时 at first 开始时 not at all 一点也不 2、about ①表示大约时间： I's about six o'clock now. 现在大约6点钟了。 ②表示地点；在……周围： Everthing about me is so beautiful 我周围的一切都那么美好 ③关于，对于： We are talking about the news. 我们正在谈论新闻。 3、after ①在……之后： After dinner I watch TV. 晚饭后我看电视。 ②在……后面： He came into the room after me. 他在我后面进了房间。 4、behind ①在……之后： There is a bike behind the tree. 树后有一辆自行车 ②比……晚，迟于： The train is behind time. 火车晚点了 5、by ①在……旁： He is sitting by the bed. 他正坐在床边。 ②到……时候： We have learned three English songs by now. 到现在为止，我们已经学会了三首英文歌曲。 ③以……方式： I go to school by bus. 我乘公共汽车去上学。 ④用于某些固定搭配： one by one 一个接一个 by the way 顺便说一句 6、for ①为，给，替： I'll make a card for my teacher. 我要给老师做张卡片。 ②由于： Thank you for helping me. 谢谢你帮我。 ③表示给（某人）用的： There is letter for you. 这儿有你一封信。 7、in ①在……里面： The pencil is in the desk. 铅笔在课桌里。 ②在一段时间里： We have four classes in the morning. 我们上午有四节课。 ③用，以： What's this in English 这用英语怎么说 ④在某一年份，季节，月份： in 2002, in spring, in January ⑤表示状态，服饰： Helen is in yellow. 海伦身穿黄色衣服。 ⑥在……方面： He is weak in English. 他的英语不行。 ⑦用于某些固定搭配： in front of 在……前面 in the end 最后 in time 及时 8、like ①像……样： He looks like his father. 他像他的父亲。 ②这样，那样： Don't look at me like that. 别那样看着我。

小学常见介词和介词短语

小学常见介词和介词短语 一、含义: 介词是表示两词之间的关系的词。我们在小学学过的英语介词有： 1. on (1) 在------上面The book is on the desk. (2) 在------（哪一天/星期）What do you do on Wednesday? (3) 在------（月、日）My birthday is on August 2nd. 2. in （1）在------里面The pens are in the pencil-box. ( 2 )在------（哪一年/月）His birthday is in October. He worked here in 1992. (3 ) 在------（地方）He works in Dongguan. (4 ) 在------之内What are you going to do in 20 years? (5 ) 在------（早上、下午、晚上）I do morning exercises in the morning every day. I usually play basketball in the afternoon. I often do my homework in the evening. 3. under 在------底下There is a ball under the bed. 4. near 在------附近There is a book shop near our school. 5. in front of 在------前面A boy is standing in front of the house. 6. beside 在------旁边A football is beside thedoor. 7. next to 紧挨着There is a bus station next to No. 13 Middle School. 8. over 在------正上方A bridge is over the river. 9. on the left 在------左边The bookstore is on the left. 10. on the right 在------右边The hospital is on the right. 11. before 在……之前Mike sits before me. 12. after 在------以后He went home after school. 13. in the middle 在------中间The road is in the middle. 14. at (1 ) 在------（小地方）I am at school today. I was at home yesterday. (2 ) 在------（点钟）I usually go to school at 8:00 am. （3）看一看Look at the blackboard. (4) 在中午at noon 15. behind 在------后面There is a broom behind the door. 16．For (1) 给This present is for you. (2) 为了Thank you for telling me the way to the zoo. (3) 作为We have some chips and hamburgers for lunch. 17．To (1) 到Take your sportshoes to the P.E class. (2) 致Happy birthday to you. Give it to your friend. 18. from 来自I am from China. = I come from China. 19. from --- to 从------到------ Line up from shorter to taller. We have class from Monday to Friday. 20. of ------的He is a student of Kama School. 21. by （1）在------之前We must be at home by 6 o’clock. （2）乘------交通工具People can go to the moon by spaceship. I go to school by bus.

(完整版)小学常见介词用法辨析及习题

小学常见介词用法辨析 一、介词的定义及分类 介词是一种用来表示词与词、词与句之间的关系的虚词,，在句中不能单独作句子成分。介词后面一般有名词、代词或相当于名词的其他词类，短语或从句作它的宾语。按构成分为简单介词（in、on、at等）、合成介词（into、within等）、重叠介词（at about等）、短语介词（in front of等）。 二、小学常用介词用法释义 （一）表时间 1、常用词in、on、at。 In： ①+年份/世纪。in 2019（在2019年）；In the1990s（在19世纪90年代）. ①+月份。In May（在五月）. ①+季节。In spring/summer/autumn/winter（在春/夏/秋/冬季）. ①+一天的某个时间段（上午、下午、晚上等）。In the morning/afternoon/evening at ： ①+时刻、几点。at six（在6点）/~half past ten（在10点半） ①+年龄。at thirteen/~the age of thirteen（在13岁时） ①+某个时段at noon（在中午）,at night（在晚上）, at midnight（在午夜），at dawn（在黎明） on ： ①+星期几。on Wednesday/Sunday（在星期三/在星期日）

①+日期。On June 4th =on the fourth of June （在六月4日） ①+有day的节日。On Christmas Day/Teacher’s Day（在圣诞节/教师节）①+具体某一天。On a cold day（在一个寒冷的一天）、on Sunday afternoon（在星期日下午） 2、其他常用词 Before：在...之前after：在...之后since：自从...开始for +一段时间until：直到...时候from...to：从...到...（二）表方位 1、常用词in、on、at。 In： ①在...里面：In the classroom（在教室里） ①+大地点：In China（在中国）；in Nanjing（在南京） On： ①在上面（表面）：On the desk（在桌子上） ①在左右边：On your right（在你右边） At： ①+小地点（大、小是相对而言）：at home（在家）；at the party（在宴会上）。 ①向，朝向：laugh at/shout at/point at 2、其他常见方位词