Measures in the geometric quantization of field theories

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• 作者：Olaf Mü ; ller
• 关键词：Geometric quantization ; Measure theory ; Symplectic fibre bundles ; Frechet manifolds
• 刊名：Journal of Geometry and Physics
• 出版年：2006
• 期刊代码：29_03930440
• 类别：ph
• 出版时间：2006
• 卷：56
• 期：6
• 页码：1029-1041
• 文件大小：162 K

摘要

In this article, it is shown that for the standard symplectic form on the space of compactly supported sections of a symplectic fibre bundle, there is no locally-finite Borel measure which is preserved by the Hamiltonian flows of even a quite restricted set of functions on this space. As this means that some of the operators arising in geometric quantization associated to classical observables would not be Hermitean, the result suggests that one should consider quotients by gauge groups as classical phase spaces to avoid this problem.