Driver B., Hall B.
Yang-Mills theory and the Segal-Bargmann transform
(161K, Latex 2e)
ABSTRACT. We use a variant of the classical Segal-Bargmann transform to
understand the canonical quantization of Yang-Mills theory on a
space-time cylinder. This transform gives a rigorous way to make
sense of the Hamiltonian on the gauge-invariant subspace. Our
results are a rigorous version of the widely accepted notion that
on the gauge-invariant subspace the Hamiltonian should reduce to
the Laplacian on the compact structure group. We show that the
infinite-dimensional classical Segal-Bargmann transform for the
space of connections, when restricted to the gauge-invariant
subspace, becomes the generalized Segal-Bargmann transform for
the structure group. This paper expands on the earlier paper by
the second author (mp_arc 97-580) and will appear in Communications
in Mathematical Physics.