Applications of Lie algebraic and phase space methods in quantum physics

量子力学中的相空间方法在 将抽象希尔伯特空间中定义的量子力学算符映射到 经典相空间中的复值函数适用于所考虑的系统。 这项建议涉及相空间方法在具有较高对称性的量子系统中的应用。建议的应用包括将SU(3)中已有的结果推广到具有SU(N)(和其他)对称性的系统，研究这类系统的短时半经典动力学，重点研究压缩作为短时效应，研究所谓的对应规则及其在松弛方面的可能应用，以及以相空间方法为起点研究具有较高对称性的系统的相算符。 这项工作的结果将对量子光学的物理学家--理论家和实验学家--有兴趣更好地理解量子态的一些非经典性质。

Phase space methods in quantum mechanics have in common the objective of mapping quantum mechanical operators, defined in an abstract Hilbert space, to complex-valued functions in a classical phase space appropriate for the system under consideration. This proposal deals with applications of phase space methods to quantum systems with higher symmetries. The proposed applications include the extension of results already available for SU(3) to systems with SU(n) (and other) symmetries, a study of short time semiclassical dynamics of such systems focusing on squeezing as a short time effect, an investigation of so-called correspondence rules with possible applications to relaxation, and an investigation of phase operators for systems with higher symmetries using phase space methods as a starting point. The results of this work will be of use to physicists - theorists and experimentalists - in quantum optics with an interest in a better understanding some nonclassical properties of quantum states.