arXiv subjects

K. K. Wren

Publications and source records attributed to K. K. Wren.

2 recordsLinked to original sources

arXiv1998

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

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.

math-ph↗

arXiv1997

Constrained quantization and $θ$-angles

We apply a new and mathematically rigorous method for the quantization of constrained systems to two-dimensional gauge theories. In this method, which quantizes Marsden-Weinstein symplectic reduction, the inner product on the physical state space is expressed through a certain integral over the gauge group. The present paper, the first of a series, specializes to the Minkowski theory defined on a cylinder. The integral in question is then constructed in terms of the Wiener measure on a loop group. It is shown how $þ$-angles emerge in the new method, and the abstract theory is illustrated in detail in an example.

hep-th↗