Hall B.
Yang-Mills theory and the Segal-Bargmann transform
(76K, Latex 2e)
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.