# Constrained quantization and $\\theta$-angles

Source: [Constrained quantization and $\\theta$-angles](<https://www.sota2.com/research/paper/68fa24772c2a3760193a47f0>)

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

Data updated: 2025-10-24T09:13:03.886Z

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

Published: 1997-06-25T13:45:36.000Z

## Abstract

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 $\\th$-angles emerge in the new method, and the abstract theory is illustrated in detail in an example.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-th/9706178>)

[PDF](<https://arxiv.org/pdf/hep-th/9706178.pdf>)