规范变换对求解Schrdinger方程的应用

在大部分量子力学书中都讨论了规范交换理论．并且强调指出量子力学体系的某种守恒律和规范变换的对称性具有密切的关系．考虑体系规范变换的对称性，可以使问题大大简化，并且能够得到一些有用的结果．本文利用规范变换来求解含时的 Ｓｃｈｒｏｄｉｎｇｅｒ方程．     

电磁场矢势和标势的规范变换及规范不变性的一个实例

在电磁学中,当考虑由电荷电流分布激发电磁场的问题时,引入标势（？）与矢势A给求解电磁场问题带来很大的方便,且标势（？）与矢势A满足规范变换与规范不变性.近代物理学中,规范变换是作为基本方法而引入的,     

均匀磁场中带电粒子的量子运动不违反规范不变原理

通过讨论当哈密顿算符的本征值简并对守恒量完全集的规范变换关系，说明了均匀磁场中带电粒子的量子运动不违反规范不变原理，指出了文献（１）在这个方面上得出错误结论的根源，并分析了朗道态函数在物理上的合理性。     

Fateev-Zamolodchikov量子自旋链的潜藏定域规范不变性

详细研究了自旋为1的Heisenberg XXZ模型(Fateev-Zamolodchikov模型)的潜藏定域规范不变性。发现与自旋为1/2的情形相类似,该模型允许AbelU(1)规范交换,且其能谱在规范变换下保持不变,而其本征矢却与规范变换明显相关。     

也谈含时Schrodinger方程的求解方法

利用算符对易关系的相似性和规范变换统一求解一些合时Ｓｃｈｒｄｉｎｇｅｒ方程．     

关于稳定磁场矢势的一些问题

关于稳定磁场的矢势,在一般教科书中讨论较少,现将有关的一些问题分述如下。 一、矢势的引入: 1对稳定磁场有　故可设:A即为矢势。 2.若 式中ψ为任意标量函数。则因　所以有: 此即A′仍为矢势。(2)所表示的矢势的变换称规范变换。 3.若　,利用规范变换 若使　财可有 因A′也为矢势,故利用规范变换总可以找到散度为零的矢势。 满足的矢势称矢势的库仑规范。在稳定磁场中运用矢势时,总是认为矢势满足库仑规范。 4.若　进行规范变换　,则有若使　则有:　。这就是说,在矢势满足库仑规范时,仍可进行规范变换,只是此时标量函数平需满足拉普拉斯…     

伏安法测电阻中电表内阻的修正

在大学普通物理实验中，通常采用伏安法测量电阻，电路图如图1（a）、（b）所示．图1（a）为电流表外接法，图1（b）为电流表内接法．由图1（a）知即测量值R等于被测电阻尼和电压表内阻Rv的并联值．由图1（b）知即测量值R等于被测电阻Rx和电流表内阻RA的串联值．由式（1）和式（3）可见，由于电表内阻的存在，给测量结果带来了一定的系统误差．同时，由式（2）和式（4）可以看出，如果知道了电表的内阻RV或RA，便可对测量结果进行修正．但是，在电表内阻未知的情况下，用上述方法修正测量结果时，就显得比较繁琐．另外，采用电流表的内…     

电磁学与电动力学中的磁单极-Ⅱ

本系列文章一共4篇,在电磁学和电动力学框架内用尽量科普的方式分别介绍磁单极的若干奇特性质.本篇文章主要介绍狄拉克磁单极是如何展示矢量势的规范变换的.我们首先简要介绍规范变换与规范对称性及狄拉克磁单极与狄拉克弦,然后讨论狄拉克磁单极与规范变换的联系.我们显式演示狄拉克弦摆动产生的规范变换,弦摆动区域对场点所张的立体角正比于规范变换的变换函数.磁偶极子则可以由两个无穷靠近的正反狄拉克磁单极构成.相应两条狄拉克弦位置的变化都对应磁偶极子矢量势的规范变换,特别当两条弦重合时弦效应相互抵消,只剩下纯的磁偶极子.传统的由磁偶极子产生的矢量势的规范变换则可以图像化为组成磁偶极子的正反狄拉克磁单极的狄拉克弦的摆动.我们显式地计算了位于坐标原点弦为直线的狄拉克磁单极,并进一步构造了没有奇异的吴大峻-杨振宁磁单极.     

强作用与手征规范场

本文引入了e^{ia（x）r_s定域规范变换及相应的规范场.给出了手征规范不变的拉氏函数,并由此出发探讨了手征规范场与强相互作用的联系.在特定条件下可给出唯象的V-A强相互作用形式.}     

Al掺杂对LaBa2Cu3Oy体系的物理性质的影响

利用红外光谱．电子顺磁共振以及电阻率等实验手段，对LaBa2Cu3-xAlxOy（0≤x≤0．7）系列样品进行了研究．结果表明：Al掺杂导致了体系电荷的重新分布．随着Al掺杂量的增加，超导电性被很快地抑制，电阻率逐渐增大．随着Al掺杂量的增加，Cu（1）-O（1）（530cm^-1）的伸缩振动模的强度逐渐增大，并向低频方向移动。而Cu（1）-O（4）（590cm^-1）的震动模逐渐向高频方向移动．电子顺磁共振实验（EPR）揭示了不同含量的Al掺杂对Cu^2＋的自旋关联行为的影响．本文对不同掺杂区的声子振动、自旋关联变化和输运性质进行了分析讨论．     

Action Principle and Algebraic Approach to Gauge Transformations in Gauge Theories

The action principle is used to derive, by an entirely algebraic approach, gauge transformations of the full vacuum-to-vacuum transition amplitude (generating functional) from the Coulomb gauge to arbitrary covariant gauges and in turn to the celebrated Fock–Schwinger (FS) gauge for the Abelian (QED) gauge theory without recourse to path integrals or to commutation rules and without making use of delta functionals. The interest in the FS gauge, in particular, is that it leads to Faddeev–Popov ghosts-free non-Abelian gauge theories. This method is expected to be applicable to non-Abelian gauge theories including supersymmetric ones.     

QCD Dirac spectrum and components of the gauge field

We analyze the relation between the Dirac spectrum and the gauge field in SU(3) lattice QCD. We focus on how a certain component of the gauge field is related to the Dirac spectrum. First, we consider momentum components of the gauge field. It turns out that the broad momentum region is relevant for the low-lying Dirac spectrum and topological charges. The connection with chiral random matrix theory is also discussed. Second, we consider an SU(2) subgroup component of the SU(3) gauge field. The SU(2) subgroup component behaves like the SU(2) gauge field in the low-lying Dirac spectrum.     

Propagation of self-gravitating density waves in the deDonder gauge: the physical importance of gauge solutions and the problem of initial conditions

The propagation of perturbations on a spatially flat Robertson-Walker background is studied within linear perturbation theory in deDonder gauge and for comparison in synchronous gauge. The metric perturbations should be determined uniquely by the density/pressure perturbations, therefore only two initial conditions, namely for the density contrast and its time derivative, should be needed. Since the number of fundamental solutions for the density perturbations is higher than 2 in both gauges (6 resp. 3) an additional reduction of possible initial conditions, resp. a physically motivated exclusion of solutions, is needed. It is shown that the common treatment of excluding the so-called gauge solutions (solutions which can be gauged to zero in an already chosen gauge) leads to unphysical results. If gauge solutions are excluded the density perturbation solutions are the same in both gauges. But the correct Newtonian limit — which is present in deDonder gauge but not in synchronous gauge — is bound to the differences in the two gauges for large spatial scales of perturbations. Furthermore, compressional wave solutions should vanish for infinite spatial scales of perturbations (isotropy), but this is guaranteed in deDonder gauge by gauge solutions again. Gauge solutions should therefore not be taken as unphysical.     

Dynamical supersymmetry breaking and gauge anomalies

Some aspects of supersymmetric gauge theories and discussed. It is shown that dynamical supersymmetry breaking does not occur in supersymmetric QED in higher dimensions. The cancellation of both local (perturbative) and global (non-perturbative) gauge anomalies are also discussed in supersymmetric gauge theories. We argue that there is no dynamical supersymmetry breaking in higher dimensions in any supersymmetric gauge theories free of gauge anomalies. It is also shown that for supersymmetric gauge theories in higher dimensions with a compact connected simple gauge group, when the local anomaly-free condition is satisfied, there can be at most a possibleZ ₂ global gauge anomaly in extended supersymmetricSO(10) (or spin (10)) gauge theories inD=10 dimensions containing additional Weyl fermions in a spinor representation ofSO(10) (or spin (10)). In four dimensions with local anomaly-free condition satisfied, the only possible global gauge anomalies in supersymmetric gauge theories areZ ₂ global gauge anomalies for extended supersymmetricSP(2N) (N=rank) gauge theories containing additional Weyl fermions in a representation ofSP(2N) with an odd 2nd-order Dynkin index.     

同轴圆筒形辐射真空计的绝对性

Klumb-schwarz提出的同轴圆筒形辐射真空计,原则上可以作为低气压的绝对量具,然而由于迄今并未有人提出完整的灵敏度理论,困此限制了它作为绝对量具的可能性。本文叙述一种近似解法,可以得出灵敏度的绝对值,并从理论上决定其最佳几何结构。最后还对这种真空计的量程上下限作了讨论。 关键词：     

球对称的SU2规范场和磁单极的规范场描述

本文讨论球对称的SU₂规范场,证明了满足最一般的球对称定义的SU₂规范场只能有三种基本类型:(1)同步球对称规范场;(2)狭义球对称规范场;(3)化约为U₁子群的球对称规范场。文中详细讨论了球对称的带同位旋向量场(Higgs场)的SU₂规范场,完全决定了它们的类型。如果把这种场看成为由电磁场和带电矢介子构成,那末就有如下的结论:如果磁单极所含的磁荷是最小单位的m倍,当|m|>1时,球对称的带Higgs场的SU₂规范场只能是纯电磁场,而不能有带电矢介子场出现。但当m=0,±1时,球对称的带电矢介子场是可以出现的。从而可见,具有非单位磁荷的磁单极隐含了某种破坏球对称的因素。     

Finite matrix models with continuous local gauge invariance

We construct a hamiltonian lattice gauge theory which possesses local SU (2) gauge invariance and yet is defined on a Hilbert space of 5-dimensional real vectors for every link. This construction does not allow for generalization to arbitrary SU(N), but a small variation of it can be generalized to an SU(N) × U(1) local gauge invariant model. The latter is solvable in simple gauge sectors leading to trivial spectra. We display these by studying a U(1) local gauge invariant model with similar characteristics.     

Axial-vector anomaly for Dirac-Kähler fermions on the lattice

The axial-vector current of Dirac-Kähler fermions on the lattice is studied. We consider a U(1) gauge theory in two dimensions as well as an SU(N) gauge theory in four dimensions. Using a short-distance expansion of the fermion propagator in an external gauge field, we show that the correct anomaly is reproduced in the continuum limit.     

SU(2) gauge theory of the Hubbard model: emergence of an anomalous metallic phase near the Mott critical point

We propose one possible mechanism for an anomalous metallic phase appearing frequently in two spatial dimensions, that is, local pairing fluctuations. Introducing a pair-rotor representation to decompose bare electrons into collective pairing excitations and renormalized electrons, we derive an SU(2) gauge theory of the Hubbard model as an extended version of its U(1) gauge theory. Since our effective SU(2) gauge theory admits two kinds of collective bosons corresponding to pair excitations and density fluctuations, respectively, an intermediate phase appears naturally between the spin liquid Mott insulator and Fermi liquid metal of the U(1) gauge theory, characterized by softening of density-fluctuation modes as the Fermi liquid, but gapping of pair-excitation modes. We show that this intermediate phase is identified with an anomalous metallic phase because there are no electronlike quasiparticles although it is metallic.