高阶微商系统Dirac猜想的一个反例

由扩展正则作用量导出了高阶微商奇异Lagrange量系统的扩展正则Noether恒等式.从广义约束Hamilton系统相空间中对称性分析，给出高阶微商系统Dirac猜想的一个反例. 用正则Noether定理、 正则Noether恒等式和扩展正则Noether恒等式说明在此反例中Dirac猜想失效, 讨论中没有将约束线性化. 关键词： 高阶微商系统 约束Hamilton系统 正则对称性 Dirac猜想     

高阶微商场论中奇异拉氏量系统的量子正则对称性

给出了高阶徽商场论中奇异拉氏量系统规范生成元的构成.从相空间中Green函数的生成泛函出发,导出了约束Hamilton系统正则形式的Ward恒等式.指出该系统的量子正则方程与由Dirac猜想得到的经典正则方程不同.给出了与Chern-Simons理论等价的一个广义动力学系统的量子化.将正则Ward恒等式初步应用于该系统,不作出对正则动量的路径积分,也可导出场的传播子与正规顶角之间的某些关系.     

约束系统正则形式的对称性质

本文导出场论中用奇异拉氏量描述的系统正则形式的广义Noether第一定理(GNFT),导出无限连续群下变更性系统正则形式的广义Noether恒等式(GNI),讨论了它们在Dirac约束理论中的应用。给出一个新的反倒,说明Dirac猜想失效,指出某些变更性系统也具有Dirac约束,讨论了GNI在色动力学中的应用。 关键词：     

约束系统量子化中Dirac方法与Faddeev-Jackiw方法的等价性

对约束系统量子化中Dirac方法和 Faddeev-Jackiw方法进行了讨论，并对它们的运动方程、正则量子化的等价性进行证明.找出了两种方法中约束的对应关系. 关键词： Faddeev-Jackiw方法 Dirac方法 约束系统 正则量子化     

有限空间中Dirac场的正则量子化

研究当存在边界的情形下 Dirac场的正则量子化问题. 采用文献[1]的观点, 将边界条件当作Dirac初级约束.与已有研究不同的是, 本文从离散的角度研究此问题. 将Dirac场的拉氏量和内在约束进行离散化, 并且将离散的边界条件当作初级Dirac约束. 因此, 从约束的起源来看, 这个模型中存在两种不同的约束: 一种是由于模型的奇异性而带来的约束, 即内在约束; 另一种是边界条件. 在对此模型进行正则量子化过程中提出一种能够平等地处理内在约束和边界条件的方法. 为了证明该方法能够平等地对待这两种起源不同的约束, 在计算Dirac 括号时分别选取了两个不同的子集合来构造"中间Dirac括号", 最后得到了相同的结果. 关键词： 边界条件 Dirac约束 Dirac括号     

奇异系统Hamilton正则方程的Mei对称性、Noether对称性和Lie对称性

研究奇异系统Hamilton正则方程的形式不变性即Mei对称性，给出其定义、确定方程、限制方程和附加限制方程.研究奇异系统Hamilton正则方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明结果的应用. 关键词： 奇异系统 Hamilton正则方程 约束 对称性 守恒量     

仅含第二类约束的约束Hamilton系统的Lie对称性

研究仅含第二类约束的约束Hamilton系统的Lie对称性.建立Lie对称性的确定方程、限制方程和附加限制方程,给出由Lie对称性导致守恒量的条件及守恒量的形式 关键词： 奇异系统 正则变量 约束 Lie对称性 守恒量     

非保守力和非完整约束对Hamilton系统Lie对称性的影响

研究非保守力和非完整约束对Hamilton系统的Lie对称性和守恒量的影响.分别研究了Hamilt on系统受到非保守力和非完整约束作用时，系统的Lie对称性保持不变的条件，同时给出了 系统的结构方程和守恒量保持不变的条件.以著名的Emden方程和Appell-Hamel模型为例进行 了分析讨论. 关键词： 分析力学 Hamilton系统 非保守力 非完整约束 对称性 守恒量     

关于Lagrange系统和Hamilton系统的Mei对称性

对Lagrange 系统和Hamilton系统Mei对称性的研究表明，Mei对称性的两种表述对Lagrange系统是等价的，给出一类Mei对称性，而对Hamilton系统不等价，给出两类Mei对称性. 关键词： Lagrange系统 Hamilton系统 Mei对称性 守恒量     

正则Ward恒等式和Abel规范理论中动力学质量的产生

文中基于约束Hamilton系统理论用Faddeev-Senjanovic路径积分量子化方法,重新讨论了Cornwall-Norton和Jackiw-Johnson模型的量子化,导出了这两个系统的正则Ward恒等式,利用导出的正则Ward恒等式,得到了包括费米子和束缚态的质量谱.所得的结果与其他方法导出的结果相同     

On Dirac''s Conjecture

The extended canonical Noether identities and canonical first Noether theorem derived from an extended action in phase space for a system with a singular Lagrangian are formulated. Using these canonical Noether identities, it can be shown that the constraint multipliers connected with the first-class constraints may not be independent, so a query to a conjecture of Dirac is presented. Based on the symmetry properties of the constrained Hamiltonian system in phase space, a counterexample to a conjecture of Dirac is given to show that Dirac's conjecture fails in such a system. We present here a different way rather than Cawley's examples and other's ones in that there is no linearization of constraints in the problem. This example has a feature that neither the primary first-class constraints nor secondary first-class constraints are generators of the gauge transformation.     

Generalized Canonical Noether Theorem and Poincare—Cartan Integral Invariant ofr a System with a Singular High—Order Lagrangian and an Application

Based on the canonical action,a generalized canonical first Noether theorem and Poicare-Cartan integralinvariant for a system with a singular high-order Lagrangian are derived.It is worth while to point out that the constraints are invariant under the total variation of canonical variables including time.We can also deduce the result,which differs from the previous work to reuire that the constraints are invariant under the simultaneous variations of canonical variables.A counter example to a conjecture of the Dirac for a system with a singular high-order Lagrangian is given,in which there is no linearization of constraint.     

Generalized Noether theorems in canonical formalism for field theories and their applications

A generalization of Noether's first theorem in phase space for an invariant system with a singular Lagrangian in field theories is derived and a generalization of Noether's second theorem in phase space for a noninvariant system in field theories is deduced. A counterexample is given to show that Dirac's conjecture fails. Some preliminary applications of the generalized Noether second theorem to the gauge field theories are discussed. It is pointed out that for certain systems with a noninvariant Lagrangian in canonical variables for field theories there is also a Dirac constraint. Along the trajectory of motion for a gauge-invariant system some supplementary relations of canonical variables and Lagrange multipliers connected with secondary first-class constraints are obtained.     

APPROXIMATE PARTIAL NOETHER OPERATORS OF THE SCHWARZSCHILD SPACETIME

The objective of this paper is twofold: (a) to find a natural example of a perturbed Lagrangian that has different partial Noether operators with symmetries different from those of the underlying Lagrangian. First we regard the Schwarzschild spacetime as a perturbation of the Minkowski spacetime and investigate the approximate partial Noether operators for this perturbed spacetime. It is shown that the Minkowski spacetime has 12 partial Noether operators, 10 of which are different from the 17 Noether symmetries for this spacetime. It is found that for the perturbed Schwarzschild spacetime we recover the exact partial Noether operators as trivial first-order approximate partial Noether operators and there is no non-trivial approximate partial Noether operator as for the Noether case. As a consequence we state a conjecture. (b) Then we prove a conjecture that the approximate symmetries of a perturbed Lagrangian form a subalgebra of the approximate symmetries of the corresponding perturbed Euler–Lagrange equations and illustrate it by our examples. This is in contrast to approximate partial Noether operators.     

Generalized Noether theorems and applications

We generalize the first and second Noether theorems (Noether identities) to a constrained system in phase space. As an example, the conservation law deriving from Lagrange's formalism cannot be obtained fromH _E via the generalized first Noether theorem (GFNT); Dirac's conjecture regarding secondary first-class constraints (SFCC) is invalid in this example. A preliminary application of the generalized Noether identities (GNI) to nonrelativistic charged particles in an electromagnetic field shows that on the constrained hypersurface in phase space one obtains electric charge conservation. This conservation law is valid whether Dirac's conjecture holds true or not.     

Classification of first-order Lagrangians on the line

We present a complete classification for first-order Lagrangians defined on the line according to the Noether point symmetry algebra they admit. All possible canonical forms of Lagrangians that admit Noether algebras are given.     

Killing and Noether Symmetries of Plane Symmetric Spacetime

This paper is devoted to investigate the Killing and Noether symmetries of static plane symmetric spacetime. For this purpose, five different cases have been discussed. The Killing and Noether symmetries of Minkowski spacetime in cartesian coordinates are calculated as a special case and it is found that Lie algebra of the Lagrangian is 10 and 17 dimensional respectively. The symmetries of Taub’s universe, anti-deSitter universe, self similar solutions of infinite kind for parallel perfect fluid case and self similar solutions of infinite kind for parallel dust case are also explored. In all the cases, the Noether generators are calculated in the presence of gauge term. All these examples justify the conjecture that Killing symmetries form a subalgebra of Noether symmetries (Bokhari et al. in Int. J. Theor. Phys. 45:1063, 2006).     

Symmetry in extended phase space for singular Lagrangian with subsidiary constraints

A generalization of the Noether theorem to a singular nonholonomic system in the canonical formalism is given and its inverse theorem is presented. Based on the canonical action integral, a generalization of the Poincaré-Cartan integral invariant of a singular nonholonomic system is obtained. It is shown that this invariant is equivalent to the canonical equations of a singular constrained system. Some confusions in the literature are corrected. An example is given.     

非定域量子Noether恒等式及应用

基于高阶微商奇异拉氏量系统的相空间生成泛函,导出了定域和非定域变换下的量子正则Noether恒等式;对高阶微商规范不变系统,导出了位形空间中定域和非定域变换下的量子Noether恒等式.指出在某些情形下,由量子Noether恒等式可导致系统的量子守恒律.这种求守恒律的程式与量子Noether(第一)定理不同.用于高阶微商非AbelChern-Simons(CS)理论,求出某些非定域等变换下的量子守恒量.