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

The Erwin Schrr Odinger International Institute for Mathematical Physics Combinatorial Quantization of the Hamiltonian Chern-simons Theory Combinatorial Quantization of the Hamiltonian Chern-simons Theory

Motivated by a recent paper of Fock and Rosly 6] we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which reproduces the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Ham...

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...

Running Coupling in Pure Gauge Theories Using the Schr¨odinger Functional

Schrödinger functional, the propagation kernel for going from some field configuration at time x 0 = 0 to some other configuration at x 0 = T , is used to define a running coupling, ¯ g 2 (L), at a length scale, L, in pure gauge theories. Using a lattice formulation and finite size scaling techniques, this running coupling is calculated non-perturbatively in the continuum for a wide range of L,...

The Erwin Schrr Odinger International Institute for Mathematical Physics Field Theory on a Supersymmetric Lattice Field Theory on a Supersymmetric Lattice 1

A lattice-type regularization of the supersymmetric eld theories on a supersphere is constructed by approximating the ring of scalar superrelds by an integer-valued sequence of nite dimensional rings of supermatrices and using the diierencial calculus of non-commutative geometry. The regulated theory involves only nite number of degrees of freedom and is manifestly supersymmetric.

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