高阶微商系统中正则Ward恒等式和Abel规范理论中动力学质量的产生

基于含复合场的正则Ward恒等式，研究了含高阶微商的Abel理论中动力学规范对称破缺.得到了包括费米子和束缚态的质量谱.讨论了高阶微商项的影响. 关键词： 正则Ward恒等式 约束 动力学对称破缺 Abel规范理论     

Algebraic integrability and generalized symmetries of dynamical systems

It has been shown that when an n-dimensional dynamical system admits a generalized symmetry vector field which involves a divergence-free Liouville vector field, then it possesses n−1 independent first integrals (i.e., it is algebraically integrable). Furthermore, the Liouville vector field can be employed for the classification of algebraically integrable dynamical systems. The results have been discussed on examples which arise in physics.     

Noether symmetries of discrete nonholonomic dynamical systems

In this letter, we investigate Noether symmetries and conservation laws of discrete dynamical systems on an uniform lattice with the nonholonomic constraints. Based on the quasi-invariance of discrete Hamiltonian action of the systems under the infinitesimal transformation with respect to the time and generalized coordinates, we give the discrete analogue of generalized variational formula of the systems. From this formula we derive the discrete analogue of generalized Noether-type identity, and then we present the generalized quasi-extremal equations of the systems. We also obtain the discrete analogue of Noether theorems and the discrete analogue of Noether conservation laws of the systems. Finally, an example is discussed to illustrate these results.     

Nonlinear dynamical symmetries of Smorodinsky–Winternitz and and Fokas–Lagerstorm systems

General solutions of the Smorodinsky–Winternitz system and the Fokas–Lagerstorm system, which are superintegrable in two-dimensional Euclidean space, are obtained using the algebraic method (structure function). Their dynamical symmetries, which are governed by deformed angular momentum algebras, are revealed.     

Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system.On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation,the determining equations,the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed.The criterions of Mei symmetries,weak Mei symmetries and strong Mei symmetries of the system are given.New types of conserved quantities,i.e.the Mei symmetrical conserved quantities,the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system,are obtained.Then,a deduction of the first-order nonholonomic system is discussed.Finally,two examples are given to illustrate the application of the method and then the results.     

Clusterization and dynamical symmetries

A variety of dynamical symmetries related to nuclear clusterization is discussed.     

Velocity-dependent symmetries and conserved quantities of the constrained dynamical systems

In this paper, we have extefided the theorem of the velocity-dependent symmetries to nonholonomic dynamical systems. Based on the infinitesimal transformations with respect to the coordinates, we establish the determining equations and restrictive equation of the velocity-dependent system before the structure equation is obtained. The direct and the inverse issues of the velocity-dependent symmetries for the nonholonomic dynamical system is studied and the non-Noether type conserved quantity is found as the result. Finally, we give an example to illustrate the conclusion.     

Hamiltonian reduction and unfolding of dynamical systems with gauge symmetries

We investigate the reduction and unfolding of dynamical systems with gauge symmetries. An application is provided by a non relativistic point charge in the field of a Dirac monopole. The corresponding dynamical system possessing a Kepler type symmetry is associated with the Taub-NUT metric using a reduction procedure of symplectic manifolds with symmetries. The reverse of the reduction procedure is done by stages performing the unfolding of the gauge transformation followed by the Eisenhart lift in connection with scalar potentials.     

Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems

This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomicdynamicM systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equationsand restrictive equations and give three definitions of Lie symmetries before the structure equations and conservedquantities of tile Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example ispresented for illustrating the results.     

Matter stability in modified teleparallel gravity

We study the matter stability in modified teleparallel gravity or f(T)$f(T)$ theories. We show that there is no Dolgov–Kawasaki instability in these types of modified teleparallel gravity theories. This gives for the f(T)$f(T)$ theories a great advantage over their f(R)$f(R)$ counterparts because from the stability point of view there isn?t any limit on the form of functions that can be chosen.     

Non-Noether symmetries and Lutzky conservative quantities of nonholonomic nonconservative dynamical systems

Non-Noether symmetries and conservative quantities of nonholonomic nonconservative dynamical systems are investigated in this paper. Based on the relationships among motion, nonconservative forces, nonholonomic constrained forces and Lagrangian, non-Noether symmetries and Lutzky conservative quantities are presented for nonholonomic nonconservative dynamical systems. The relation between non-Noether symmetry and Noether symmetry is discussed and it is further shown that non-Noether conservative quantities can be obtained by a complete set of Noether invariants. Finally,an example is given to illustrate these results.     

Stationary axisymmetric fields in a teleparallel theory of gravitation

The existence of a set of tetrads satisfying the Møller equations and leading to the Kerr metric is proved by using a particular procedure, which could be very useful to deal with other stationary axisymmetric cases of general relativity in the framework of Møller's theory of gravitation.     

Novel symmetries in the modified version of two dimensional Proca theory

The European Physical Journal C - We present a study of the expected precision of the top quark mass determination, measured at a linear e + e − collider based on CLIC technology....     

一类动力学方程的Mei对称性

研究一类动力学方程的Mei对称性的定义和判据，由Mei对称性通过Noether对称性可找到Noether守恒量.由Mei对称性通过Lie对称性可找到Hojman守恒量.同时，也可找到一类新型守恒量.     

Continuum analogues of contragredient Lie algebras (Lie algebras with a Cartan operator and nonlinear dynamical systems)

We present an axiomatic formulation of a new class of infinitedimensional Lie algebras-the generalizations ofZ-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras continuum Lie algebras. The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered.     

Autonomous systems,dynamical systems,LPTI symmetries,topology of trajectories,and periodic solutions

In the case of autonomous dynamical systems, it is better to base symmetry considerations on trajectories than on full solutions. In this setting topological arguments can be used; a special role is played in this context by time-independent Lie-point symmetries. As an application of this approach, we obtain results on the existence of stationary and/or periodic solutions.     

Recursion operators, higher-order symmetries and superintegrability in quantum mechanics

A connection between the theory of superintegrable quantum-mechanical systems, which admit a maximal number of integrals of motion, and the standard Lie group theory is established. It is shown that the flows generated by first- and second-order Lie symmetries of the bidimensional Schrödinger equation can be classified and interpreted as quantum-mechanical operators which commute with integrable or superintegrable Hamiltonians. In this way, all known superintegrable potentials in the plane are naturally obtained and slightly more general integrals of motion are found.