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关于量子Poincaré-Cartan积分不变量
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作者 李瑞洁 李子平 《北京工业大学学报》 CAS CSCD 北大核心 2001年第2期187-190,201,共5页
基于相空间Green函数的生成泛函,导出了普遍情况下正规Lagrange量系统和奇异 Lagrange量系统的量子Poincaré-Cartan(PC)积分不变量.证明了该不变量与量子正则方程等价.当变换的Jac... 基于相空间Green函数的生成泛函,导出了普遍情况下正规Lagrange量系统和奇异 Lagrange量系统的量子Poincaré-Cartan(PC)积分不变量.证明了该不变量与量子正则方程等价.当变换的Jacobi行列式不为1时,仍可导出量子PC积分不变量;这与量子Noether定理不同.并将量子PC积分不变量与经典情况作了对比.结果表明:经典和量子PC积分不变量成立的条件和表达式均不同. 展开更多
关键词 路径积分 生成泛函 量子poincare-cartan积分不变量
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Generalized Canonical Noether Theorem and Poincare—Cartan Integral Invariant ofr a System with a Singular High—Order Lagrangian and an Application
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作者 LIZi-Ping LIRui-Jie 《Communications in Theoretical Physics》 SCIE CAS CSCD 2001年第2期157-162,共6页
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 c... 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. 展开更多
关键词 哈密顿系统 poincare-cartan积分不变性 力学系统
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Generalized Noether Theorem and Poincaré-Cartan Integral Invariant for Singular High-order Lagrangian in Fields Theories 被引量:2
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作者 李子平 《Science China Mathematics》 SCIE 1993年第10期1212-1225,共14页
A generalized first Noether theorem (GFNT) originating from the invariance under the finite continuous group for singular high-order Lagrangian and a generalized second Noether theorem (or generalized Noether identiti... A generalized first Noether theorem (GFNT) originating from the invariance under the finite continuous group for singular high-order Lagrangian and a generalized second Noether theorem (or generalized Noether identities (GNI)) for variant system under the infinite continuous group of field theory in canonical formalism are derived. The strong and weak conservation laws in canonical formalism are also obtained. It is pointed out that some variant systems also have Dirac constraint. Based on the canonical action, the generalized Poincaré-Cartan integral invariant (GPCⅡ) for singular high-order Lagrangian in the field theory is deduced. Some confusions in literafure are clarified. The GPCⅡ connected with canonical equations and canonical transformation are discussed. 展开更多
关键词 NOETHER theorem poincare-cartan INTEGRAL INVARIANT HIGH-ORDER derivatives theories in field theories Dirac’s theory of constrained system.
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