The Erwin Schrr Odinger International Institute for Mathematical Physics Projective Techniques and Functional Integration for Gauge Theories Projective Techniques and Functional Integration for Gauge Theories

Projective Techniques and Functional Integration for Gauge Theories

A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, infinite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used...

The Erwin Schrr Odinger International Institute for Mathematical Physics Lattice Gauge Fields and Noncommutative Geometry Lattice Gauge Fields and Noncommutative Geometry

Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its elds. In this paper, we develop a formulation which tries to remedy this defect. It starts from a cubical decomposition of the supporting manifold (compacti ed spacetime or spatial slice) interpreting it as a nite topological approximation in the sense of Sorkin. This nite space is ent...

The Erwin Schrr Odinger International Institute for Mathematical Physics Diierential Geometry on the Space of Connections via Graphs and Projective Limits Diierential Geometry on the Space of Connections via Graphs and Projective Limits

In a quantum mechanical treatment of gauge theories (including general relativity), one is led to consider a certain completion, A=G, of the space A=G of gauge equivalent connections. This space serves as the quantum connguration space, or, as the space of all Euclidean histories over which one must integrate in the quantum theory. A=G is a very large space and serves as a \universal home" for ...

The Erwin Schrr Odinger International Institute for Mathematical Physics Finite Gauge Model on the Truncated Sphere Finite Gauge Model on the Truncated Sphere 1

The Erwin Schrr Odinger International Institute for Mathematical Physics A-1090 Wien, Austria Su Q (2) Lattice Gauge Theory Su Q (2) Lattice Gauge Theory

We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, it then gets promoted to a quantum group gauge symmetry. The theory depends on two parameters-the deformation parameter and the lattice spacing a. We show that the system of Kogut and Susskind is ...