相空间中离散完整系统的Noether对称性和Mei对称性

研究相空间中离散完整系统的Noether对称性、Mei对称性及其导致的守恒量.利用差分离散变分方法,给出相空间中离散完整系统的差分离散变分原理,建立系统的离散正则方程和能量演化方程;给出系统Noether对称性和Mei对称性的判定条件,得到系统离散形式的Noether守恒量和Mei守恒量及其存在的条件.举例说明结果的应用. 关键词： 相空间 离散完整系统 对称性 守恒量     

Lie symmetry and Mei symmetry of a rotational relativistic system in phase space

The Lie symmetry and the Mei symmetry of a rotational relativistic system in phase space are studied. The definition, criterion and conserved quantity of the Lie symmetry and the Mei symmetry of a rotational relativistic system in phase space are given. The relation between the Lie symmetry and the Mei symmetry is found. An example is given to illustrate the application of the result.     

相空间中力学系统的Lie-Mei对称性

研究了相空间中力学系统的一种新对称性——Lie-Mei对称性及其守恒量. 提出这种新对称性的定义, 给出了系统Lie-Mei对称性的判据, 得到了系统Lie-Mei对称性导致的广义Hojman守恒量和Mei守恒量. 举例说明了结果的应用. 关键词： 相空间 力学系统 Lie-Mei对称性 守恒量     

Noether——Lie symmetry and conserved quantities of mechanical system in phase space

In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether--Lie symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the generalized Hojman conserved quantity of the Noether--Lie symmetry of the system are obtained. The Noether--Lie symmetry contains the Noether symmetry and the Lie symmetry, and has more generalized significance.     

Bradyon-luxon symmetry

We propose a spacetime scheme representing the union of the real and non-real spacetime as a possible geometrical framework for Caldirola’s idea, that the bradyonic motion can be regarded as a light-like motion in an additional extra space. The playground of all physical processes is the union space. However, the physical processes in union space are differently projected on the real and non-real spacetime. The waves linked with luxons in union space are projected on the real spacetime so that they propagate here always with the velocity of light. The waves linked with bradyons in union space are projected on the non-real spacetime so that they propagate here with the velocity of light. The wave linked with a bradyon in union space, which is projected on the real spacetime, is here described by the Schroedinger and Dirac equations. There is proposed a symmetry which demands that the physical world is in its law the same whether it is seen from real or non-real spacetime. We discuss some consequences of this symmetry in the theory of elementary particles.     

A unified symmetry of nonholonomic mechanical systems in phase space

In this paper, we have studied the unified symmetry of a nonholonomic mechanical system in phase space. The definition and the criterion of a unified symmetry of the nonholonomic mechanical system in phase space are given under general infinitesimal transformations of groups in which time is variable. The Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity are obtained from the unified symmetry. An example is given to illustrate the application of the results.     

New conserved quantities of Noether--Mei symmetry of mechanical system in phase space

This paper studies two new types of conserved quantities deduced by Noether Mei symmetry of mechanical system in phase space. The definition and criterion of Noether Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether- Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether Mei symmetry of mechanical system can be obtained.     

非对易时空中的量子场论及其唯象学

首先介绍非对易时空量子场论的基本思想, 并简短地回顾直线对撞机上的唯象学研究. 然后, 较详细地讨论通过e⁺e^－碰撞的中性Higgs粒子对产生来探测非对易信号, 及如何利用洛仑兹对称性破坏从标准模型背景中分离出信号. 最后, 简要地提及构造现实模型方面的近期进展.     

相空间中变质量力学系统Lie-Mei对称性的两个守恒量

研究相空间中变质量力学系统Lie-Mei对称性导致的两个守恒量,给出系统Lie-Mei对称性的定义和判据,引入谐调函数,得到系统Lie-Mei对称性导致的两个守恒量的条件和形式,并给出应用算例. 由于谐调函数可根据寻找规范函数的需要适当选取,且选取具有多样性,因此能够找到系统Lie-Mei对称性更多的守恒量. 关键词： 相空间 变质量系统 Lie-Mei对称性 守恒量     

A new type of conserved quantity of Mei symmetry for relativistic nonholonomic mechanical system in phase space

In this paper, a new type of conserved quantity induced directly from the Mei symmetry for a relativistic nonholonomic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for the existence and form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.     

非对易相空间三模坐标动量耦合谐振子的能谱

本文用不变本征算符方法研究非对易相空间中三模坐标动量耦合谐振子的能谱,分别得到了非耦合和坐标动量耦合两种情况下谐振子能谱的解析解,其中包括受非对易参数θ和φ影响的解λ0,1和λ1,1,以及不受非对易参数θ和φ影响的解λ0,2和λ1,2.然后,分析了两类耦合参数κ和η对三模坐标动量耦合谐振子能谱的影响.结果发现,耦合参数κ和η对λ1,1的影响是相同的,且当κ=η时,耦合系数κ和η对λ1,1是没有影响的.     

相空间中变质量力学系统的Hojman守恒量

研究一般的无限小变换下相空间中变质量力学系统Lie对称性的Hojman守恒量. 给出了相空 间中变质量力学系统Lie 对称性的确定方程和Hojman守恒量定理,并举例说明结果的应用. 关键词： 相空间 变质量系统 一般的无限小变换 Lie对称性 Hojman守恒量     

非对易空间中耦合谐振子的能级分裂

非对易空间效应的出现引起了物理学界的广泛兴趣。 介绍了非对易空间中量子力学的代数关系,在所考虑的空间变量的对易关系中包含了坐标 坐标的非对易性, 并且把 Moyal-Weyl 乘法在非对易空间中通过一个Bopp变换转变成普通的乘法。 然后给出了非对易空间中耦合谐振子的能级分裂情况。 The effect of noncommutativity of space have caused the physical academic circles widespread interest. In this paper, the non commutative (NC) is introduced, which contain non commutative of coordinate coordinate, and find that the Moyal Weyl product in NC space can be replaced with a Bopp shift. Then, the energy splitting of the coupling harmonic oscillator in non commutative spaces are discussed.     

相空间中离散力学系统对称性的摄动与Hojman型绝热不变量

研究相空间中离散力学系统对称性的摄动与绝热不变量.列出相空间中未受扰离散力学系统的特殊Lie对称性导致的Hojman型精确不变量.基于相空间中力学系统的高阶绝热不变量的定义，研究在小扰动作用下系统Lie对称性的摄动，得到了相空间中离散力学系统的一类新的绝热不变量——Hojman型绝热不变量.举例说明结果的应用. 关键词： 相空间 Lie对称性 摄动 绝热不变量     

Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.     

Investigation of Fermions in Non-commutative Space by Considering Kratzer Potential

The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, we have obtained the Wigner function corresponding to the eigenfunctions.     

New non-Noether conserved quantities of mechanical system in phase space

This paper focuses on studying non-Noether conserved quantities of Lie symmetry and of form invariance for a mechanical system in phase space under the general infinitesimal transformation of groups. We obtain a new non-Noether conserved quantity of Lie symmetry of the system, and Hojman and Mei's results are of special cases of our conclusion. We find a condition under which the form invariance of the system will lead to a Lie symmetry, and, further, obtain a new non-Noether conserved quantity of form invariance of the system. An example is given finally to illustrate these results.     

相空间中力学系统的两类Mei对称性及守恒量

研究相空间中力学系统的两类Mei对称性及守恒量，给出相空间中力学系统的两类Mei对称性的定义，得到其确定方程及守恒量，并举例说明结果的应用. 关键词： 相空间 力学系统 Mei对称性 守恒量     

Interference phase of mass neutrino in Reissner-NordstrSm-de Sitter space-time

The chemical potential of electrons in a strong magnetic field is investigated. It is shown that the magnetic field has only a slight effect on electron chemical potential when B < 1011 T, but electron chemical potential will decrease greatly when B > 1011 T. The effects of a strong magnetic field on electron capture rates for 60Fe are discussed, and the result shows that the electron capture sharply decreases because of the strong magnetic field.