相对论与量子力学概念的倒易对称性与等价性

Group analysis approach for finding reciprocal transformations for the two-dimensional stationary gasdynamics

Equivalence transformations play one of the important roles in continuum mechanics. These transformations reduce the original equations to simpler forms. One of the classes of nonlocal equivalence transformations is the class of reciprocal transformations. Despite the long history of applications of such transformations in continuum mechanics, there is no method of obtaining them. Recently such a method was proposed by the second author of the present paper. The method uses group analysis approach and it consists of similar steps as for finding an equivalence group of transformations. The new …

Miura-互反变换与可局部化的Poisson束

Miura-reciprocal transformations and localizable Poisson pencils

本文证明Miura-互反群下可局部化半单Poisson束的形变等价类含局部代表，并与Miura群下局部半单Poisson束的形变等价类一一对应。

On the quantization of mechanical systems

We present a canonical way of assigning to each magnitude of a classical mechanical system a differential operator in the configuration space, thus rigorously establishing the Correspondence Principle for such systems. Here we show how each classical state given in the whole system determine, for each classical magnitude, a wave equation, whose solutions are the possible quantum states for the given state and classical magnitude. Classical states and quantum states corresponding with the same system are reciprocally conditioned.

开放热力学系统的运动方程及其与力学和电学系统的动力学等价性

Equation of Motion for Thermodynamic Systems and Their Dynamical Equivalence with Mechanical and Electrical Systems

本文通过量纲约化将热力学第一定律转化为开放系统的显式运动方程，证明其与受驱动阻尼谐振子和RLC电路动力学等价，并构建了统一的拉格朗日表述。

Unitary representations of the Galilean line group: Quantum mechanical principle of equivalence

We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these repre…

对偶性与量子力学的等价原理

Duality and the Equivalence Principle of Quantum Mechanics

根据Vafa的建议，我们提出了一个量子力学模型的S-对偶对称性观察到的量子理论的领域，弦和膜。我们的形式主义可以被理解为上半平面H的Berezin度量量化的拓扑极限，因为度量依赖性已经被去除。由于没有度量，我们的处方没有使用全局量子数。量子数只在局部产生，在选择了一个局部的真空来膨胀之后。我们的方法可以被看作是量子力学的一个明显的非微扰公式，因为我们没有把经典相空间和泊松括号作为出发点。H在SL（2，R）下的重参数化不变性导致了SL（2，R）对实现S-对偶的量子力学算符的自然作用。我们还将我们的方法与Faraggi和Matone最近提出的量子力学的等效原理联系起来。