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

Source: [Hall's coherent states, the Cameron-Martin theorem, and the quantization of Yang-Mills theory on a circle](<https://www.sota2.com/research/paper/68fa1f877a2b558e2932a5d6>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T18:46:13.054Z

Authors: N.P. Landsman, K.K. Wren

Published: 1998-12-15T13:21:04.000Z

## Abstract

We 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math-ph/9812012>)

[PDF](<https://arxiv.org/pdf/math-ph/9812012.pdf>)