arXiv math-ph/01120622001-12-31math-phmath.MP

半经典规范系统的群变换

Group Transformations of Semiclassical Gauge Systems

Oleg Shvedov

备注：: 18 pages, LaTeX

摘要：

研究了李群下对称的半经典系统。一个半经典系统的态可以看作是一个经典态X和一个量子态f在外部经典背景X中的集合（X，f）。因此，所有半经典态的集合可以被认为是一个丛（“半经典丛”）。它的基底{X}是所有经典态的集合，而纤维是外部背景X中的量子态的希尔伯特空间。半经典系统的对称变换可以看作是半经典丛的自同构。自同构群可以借助于丛的截面来研究：对于丛的任何自同构，人们赋予丛的截面的变换。研究了截面变换的无穷小性质;讨论了李群和李代数之间的对应关系。对于规范理论，半经典丛的一些点被确定：规范群作用在丛上。在这种情况下，只考虑半经典丛的规范不变截面。

英文摘要：

Semiclassical systems being symmetric under Lie group are studied. A state of a semiclassical system may be viewed as a set (X,f) of a classical state X and a quantum state f in the external classical background X. Therefore, the set of all semiclassical states may be considered as a bundle ("semiclassical bundle"). Its base {X} is the set of all classical states, while a fibre is a Hilbert space of quantum states in the external background X. Symmetry transformation of a semiclassical system may be viewed as an automorphism of the semiclassical bundle. Automorphism groups can be investigated with the help of sections of the bundle: to any automorphism of the bundle one assigns a transformation of section of the bundle. Infinitesimal properties of transformations of sections are investigated; correspondence between Lie groups and Lie algebras is discussed. For gauge theories, some points of the semiclassical bundle are identified: a gauge group acts on the bundle. For this case, only gauge-invariant sections of the semiclassical bundle are taken into account.

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摘要：

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