98-578 Driver B., Hall B.

Yang-Mills theory and the Segal-Bargmann transform (161K, Latex 2e) Aug 31, 98

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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.

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