97-580 Hall B.

Yang-Mills theory and the Segal-Bargmann transform (76K, Latex 2e) Nov 18, 97

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Abstract. I consider the canonical quantization of Yang-Mills theory on a spacetime cylinder, with the goal of obtaining an appropriate Segal-Bargmann (or coherent state) representation. I consider a variant of the CLASSICAL Segal-Bargmann transform on the space of connections, and give a simple but non-rigorous argument that on the gauge-invariant subspace this reduces to the GENERALIZED Segal-Bargmann transform for the structure group. Here the generalized Segal-Bargmann transform is the one introduced in J. Funct. Anal. 122 (1994), 103-151. The calculations also predict a new version of the generalized Segal-Bargmann transform, the properties of which are then proved by rigorous finite-dimensional methods.

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