117 research outputs found
Yang-Mills theory and the Segal-Bargmann transform
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
Greener and More Equitable: A Vision for Dams and Other Western Water Issues
10 pages.
Contains 1 page of references
Greener and More Equitable: A Vision for Dams and Other Western Water Issues
10 pages.
Contains 1 page of references
The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces
We prove the Makeenko-Migdal equation for two-dimensional Euclidean
Yang-Mills theory on an arbitrary compact surface, possibly with boundary. In
particular, we show that two of the proofs given by the first, third, and
fourth authors for the plane case extend essentially without change to compact
surfaces.Comment: Final version, minor typographical corrections. To appear in Comm.
Math. Phy
- …