ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract: The quantum field measure for gauge fields over a compact surface with boundary, with holonomy around the boundary components specified, is constructed. Loop expectation values for general loop configurations are computed. For a compact oriented surface with one boundary component, let $ be the moduli space of flat connections with boundary holonomy lying in a conjugacy class $ in the gauge group G. We prove that a certain natural closed 2-form on $ , introduced in an earlier work by C. King and the author, is a symplectic structure on the generic stratum of $ for generic $ . We then prove that the quantum Yang-Mills measure, with the boundary holonomy constrained to lie in $ , converges in a natural sense to the corresponding symplectic volume measure in the classical limit. We conclude with a detailed treatment of the case $ , and determine the symplectic volume of this moduli space.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002200050047
Permalink