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     

Canonical symmetry properties of the constrained singular generalized mechanical system

Based on generalized Apell－Chetaev constraint conditions and to take the inherent constrains for singular Lagrangian into account, the generalized canonical equations for a general mechanical system with a singular higher-order Lagrangian and subsidiary constrains are formulated. The canonical symmetries in phase space for such a system are studied and Noether theorem and its inversion theorem in the generalized canonical formalism have been established.     

Hamilton系统的Mei对称性、Noether对称性和Lie对称性

研究Hamilton系统的形式不变性即Mei对称性，给出其定义和确定方程.研究Hamilton系统的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.给出一个例子说明本文结果的应用. 关键词： Hamilton系统 Mei对称性 Noether对称性 Lie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     

Noether symmetry for fractional Hamiltonian system

Fractional Hamiltonian systems within combined Riemann-Liouville fractional order derivative and combined Caputo fractional order derivative are established. Then Noether quasi-symmetry and conserved quantity for the fractional Hamiltonian systems are presented. Thirdly, perturbation to Noether quasi-symmetry and adiabatic invariant are studied. Several special cases are discussed in each section. And finally, two applications, i.e., the fractional Lotka biochemical oscillator model and the fractional isotropic harmonic oscillator model, are discussed to illustrate the results and methods.     

广义Hamilton系统的Lie对称性与守恒量

研究广义Hamilton系统Lie对称性导致的新型守恒量.首先,建立系统的微分方程.其次,研究一类特殊无限小变换下系统的Lie对称性.第三,将Hojman定理推广到广义Hamilton系统.最后,举例说明结果的应用. 关键词： 广义Hamilton系统 Lie对称性 守恒量     

Alternative formulation in the constrained Hamiltonian system of a rigid rotator

An alternative form of the constraint characterizing the motion of a rigid rotator is introduced and is shown to lead to the same constrained Hamiltonian system as the one constructed with the conventional constraintx ²=constant. In this new formulation, the canonical pairs of phase-space variables can easily be found, and the relationx ²=constant appears through an equation of motion rather than through a constraint. Application toO(N) nonlinear sigma model is also discussed.     

The symmetry of the fundamental equations of the dynamics of a Hamiltonian system

This paper constructs covariant defining equations for infinitesimal operators of the Lie symmetry groups of the Hamilton-Jacobi equations, and Hamilton's and Lagrange's systems whose Hamiltonians are a quadratic function of the generalized momenta; a study is made of the relation between the groups, and in particular the relation is considered between the differential laws of conservation and the symmetry of the systems.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 12–16, February, 1977.     

Canonical global symmetry and quantal conservation laws for a system with singular higher order Lagrangian

Starting from the phase-space generating functional of the Green function for a system with singular higher order Lagrangian, the generalized canonical Ward identities under the global symmetry transformation in phase space is deduced. The local transformation connected with this global symmetry transformation is studied, and the quantal conservation laws are obtained for such a system. We give a preliminary application to higher derivative Yang-Mills theory; a generalized quantal BRS conserved quantity is found.     

BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transformations of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was obtained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propagators were obtained. Supported by Knowledge Innovation Project of the Chinese Academy of Sciences (Grant Nos. KJCX2-SW-N02 and KJCX2-SW-N016), the National Natural Science Foundation of China (Grant Nos. 10435080 and 10575123), Beijing Natural Science Foundation (Grant No. 1072005) and the Science and Technology Development Foundation of Beijing Municipal Education Committee (Grant No. Km200310005018)     

Chetaev型约束力学系统Appell方程的Lie对称性与守恒量

研究Chetaev型约束力学系统Appell方程的Lie对称性和Lie对称性直接导致的守恒量.分析Lagrange函数和A函数的关系;讨论Chetaev型约束力学系统Appell方程的Lie对称性导致的守恒量的一般研究方法;在群的无限小变换下,给出Appell方程Lie对称性的定义和判据;得到Lie对称性的结构方程以及Lie对称性直接导致的守恒量的表达式.举例说明结果的应用. 关键词： Appell方程 Chetaev 型约束力学系统 Lie对称性 守恒量     

广义Hamilton系统的Mei对称性导致的Mei守恒量

研究广义Hamilton系统的Mei对称性导致的守恒量. 首先,在群的一般无限小变换下给出广义Hamilton系统的Mei对称性的定义、判据和确定方程;其次,研究系统的Mei守恒量存在的条件和形式,得到Mei对称性直接导致的Mei守恒量; 而后,进一步给出带附加项的广义Hamilton系统Mei守恒量的存在定理; 最后,研究一类新的三维广义Hamilton系统,并研究三体问题中3个涡旋的平面运动. 关键词： 广义Hamilton系统 Mei对称性 Mei守恒量 三体问题     

Lie symmetry, discrete symmetry and supersymmetry of the Pauli Hamiltonian

Starting from the full group of symmetries of a system we select a discrete subset of transformations which allows to introduce the Clifford algebra of operators generating new supercharges of extended supersymmetry. The system defined by the Pauli Hamiltonian is discussed. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001 Partially supported by the KBN-Grant # 5 P03B056 20.     

Canonical and grand canonical Gibbs states for continuum systems

It is shown that for a large class of interactions any canonical Gibbs state satisfying a natural temperedness condition is a mixture of Gibbs states with appropriate activities, and vice versa. Some general results on Gibbs states and canonical Gibbs states are established. In particular, a differential characterization of Gibbs states is given.     

Canonical solutions of variational problems and canonical equations of mechanics

The canonical (non-parametric) solutions of the variational problems for integral functionals are considered and the canonical solutions of variational problems of mechanics in Minkowski spaces are derived. By combining the variational principles of least action, flow, and hyperflow canonically invariant equations for the energy-momentum variable are obtained. From these equations the equations for the action and wave functions as a general solution of the combined variational problems of mechanics are derived. These equations are applicable for describing different types of particles and interactions and are summarized within the approach of general relativity.     

The canonical equilibrium of constrained molecular models

In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. Since the maximum time step required for the stability of the dynamics is proportional to the shortest period associated with the motions of the system, constraining the fastest vibrations allows to increase it and, assuming that the added numerical cost is not too high, also increase the overall efficiency of the simulation. However, as any other element that affects the physical model, the imposition of constraints must be assessed from the point of view of accuracy: both the dynamics and the equilibrium statistical mechanics are model-dependent, and they will be changed if constraints are used. In this review, we investigate the accuracy of constrained models at the level of the equilibrium statistical mechanics distributions produced by the different dynamics. We carefully derive the canonical equilibrium distributions of both the constrained and unconstrained dynamics, comparing the two of them by means of a “stiff” approximation to the latter. We do so both in the case of flexible and hard constraints, i.e., when the value of the constrained coordinates depends on the conformation and when it is a constant number. We obtain the different correcting terms associated with the kinetic energy mass-metric tensor determinants, but also with the details of the potential energy in the vicinity of the constrained subspace (encoded in its first and second derivatives). This allows us to directly compare, at the conformational level, how the imposition of constraints changes the thermal equilibrium of molecular systems with respect to the unconstrained case. We also provide an extensive review of the relevant literature, and we show that all models previously reported can be considered special cases of the most general treatments presented in this work. Finally, we numerically analyze a simple methanol molecule in order to illustrate the theoretical concepts in a practical case.     

Non-local gauge-invariant regularization and ward identity anomalies

A gauge-invariant regularization of a massive spinor field interacting with external scalar, pseudoscalar, vector and axial fields is found. It is based on ? separating the vertices in the total Lagrangian. Rules for its use are deduced and Ward identities are written. Anomalies, present only in the divergence of the axial current, are interpreted as the high-energy contribution of the intergrals associated with some loops. They can be computed in a simple way, confirming Bardeen's result.