 98578 Driver B., Hall B.
 YangMills theory and the SegalBargmann transform
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Aug 31, 98

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Abstract. We use a variant of the classical SegalBargmann transform to
understand the canonical quantization of YangMills theory on a
spacetime cylinder. This transform gives a rigorous way to make
sense of the Hamiltonian on the gaugeinvariant subspace. Our
results are a rigorous version of the widely accepted notion that
on the gaugeinvariant subspace the Hamiltonian should reduce to
the Laplacian on the compact structure group. We show that the
infinitedimensional classical SegalBargmann transform for the
space of connections, when restricted to the gaugeinvariant
subspace, becomes the generalized SegalBargmann transform for
the structure group. This paper expands on the earlier paper by
the second author (mp_arc 97580) and will appear in Communications
in Mathematical Physics.
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