Constrained quantization and $\theta$-angles

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

34 pages, LaTeX

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• Group averaging in the (p,q) oscillator representation of SL(2,R)
• Existence of Spinorial States in Pure Loop Quantum Gravity
• Refined algebraic quantisation with the triangular subgroup of SL(2,R)
• Coherent states for compact Lie groups and their large-N limits
• Unitarity in "quantization commutes with reduction"