Yang-Mills theory and the Segal-Bargmann transform

Details Yang-Mills theory and the Segal-Bargmann transform Yang-Mills theory and the Segal-Bargmann transform

1998-08-31

arxiv.org/abs/hep-th/9808193v1

Commun.Math.Phys. 201 (1999) 249-290

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1007/s002200050555

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 the structure group.

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