 97580 Hall B.
 YangMills theory and the SegalBargmann transform
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Nov 18, 97

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Abstract. I consider the canonical quantization of YangMills theory on a
spacetime cylinder, with the goal of obtaining an appropriate
SegalBargmann (or coherent state) representation. I consider
a variant of the CLASSICAL SegalBargmann transform on the
space of connections, and give a simple but nonrigorous
argument that on the gaugeinvariant subspace this reduces to
the GENERALIZED SegalBargmann transform for the structure
group. Here the generalized SegalBargmann transform is the
one introduced in J. Funct. Anal. 122 (1994), 103151.
The calculations also predict a new version of the generalized
SegalBargmann transform, the properties of which are then
proved by rigorous finitedimensional methods.
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