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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58257We 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.14 pages, LaTeXMathematical PhysicsFunctional Analysis81T13;81R30;81Q99Hall's coherent states, the Cameron-Martin theorem, and the quantization of Yang-Mills theory on a circletext