Yang-Mills theory and the Segal-Bargmann transform

Aug, 1998
40 pages
Published in:
  • Commun.Math.Phys. 201 (1999) 249-290
e-Print:

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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 the structure group.
  • gauge field theory: Yang-Mills
  • Segal-Bargmann transformation
  • space-time: cylinder
  • measure
  • holonomy
  • quantization
  • analysis: stochastic
  • mathematical methods