Hall's coherent states, the Cameron-Martin theorem, and the quantization of Yang-Mills theory on a circle

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dc.creatorLandsman, N. P.
dc.creatorWren, K. K.
dc.date1998-12-15
dc.date.accessioned2026-07-07T04:32:37Z
dc.date.available2026-07-07T04:32:37Z
dc.descriptionWe discuss the classical and quantum reduction to the space of physical degrees of freedom of Yang--Mills theory on a circle (so that space-time is a cylinder). Although the classical reduced phase space is finite-dimensional, the quantum reduction procedure is mathematically fascinating, involving firstly the Wiener measure on a loop group, secondly a generalization of the Cameron--Martin theorem to loop groups, and thirdly Hall's coherent states for compact Lie groups. Our approach is based on a quantum analogue of the classical Marsden--Weinstein symplectic reduction process.
dc.description14 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math-ph/9812012
dc.identifierhttp://arxiv.org/abs/math-ph/9812012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58257
dc.subjectMathematical Physics
dc.subjectFunctional Analysis
dc.subject81T13;81R30;81Q99
dc.titleHall's coherent states, the Cameron-Martin theorem, and the quantization of Yang-Mills theory on a circle
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