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29 March 2024
 
  » arxiv » hep-th/9808193

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Yang-Mills theory and the Segal-Bargmann transform
Bruce K. Driver ; Brian C. Hall ;
Date 31 Aug 1998
Journal Commun.Math.Phys. 201 (1999) 249-290
Subject High Energy Physics - Theory; Mathematical Physics | hep-th math-ph math.MP
AbstractWe 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.
Source arXiv, hep-th/9808193
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