Some comments on Laplacian gauge fixing

Laplacian gauge fixing was introduced to find a unique representative of the gauge orbit, which on the lattice could be implemented by a ``finite'' algorithm. What was still lacking was a perturbative formulation of this gauge, which will be presented here. However, renormalizability is still to be demonstrated. For torodial and spherical geometries a detailed comparison with the Landau (or Coulomb) gauge will be made.Comment: Contribution to Lattice '94, 3 pages PostScrip

Monte Carlo calculation for systems consisting of several coordinate patches

I investigate the time step dependence of Monte Carlo simulations for coordinate-spaces consisting of several patches. It is shown that a naive kinetic term does not necessarily converge to the same spectrum as a Hamiltonian calculation. Then an improved kinetic term is presented which allows one to connect the Monte Carlo and Rayleigh-Ritz results of intermediate volume SU(2) gauge theory.Comment: 18 page

Instanton Moduli for T**3xR

We review the specific problems that arise when studying instantons on a torus. We discuss how the Nahm transformation shows that no exact charge one instanton on T**4 can exist. However, taking one of the directions (the time) to infinity, it can be shown that vacuum to vacuum tunnelling solutions exist. A precise description of the moduli space for T**3xR, studied numerically using lattice techniques, remains an interesting open problem. New is an explicit application of the Nahm transformation to (anti-)selfdual constant curvature solutions on T**4 and a discussion of its properties relevant to instantons on T**3xR.Comment: 12p with 3 figs, uufiles -gz format. Talk at the 29th Int. Symp. on the Theory of Elem. Part., Buckow, 29 Aug.-2 Sept., 1995

One-loop effective action for SU(2) gauge theory on S^3

We consider the effective theory for the low-energy modes of SU(2) gauge theory on the three-sphere. By explicitely integrating out the high-energy modes, the one-loop correction to the hamiltonian for this problem is obtained. We calculate the influence of this correction on the glueball spectrum.Comment: 12p. latex, 3 PostScript figures included (epsf

Zooming-in on the SU(2) fundamental domain

For SU(2) gauge theories on the three-sphere we analyse the Gribov horizon and the boundary of the fundamental domain in the 18 dimensional subspace that contains the tunnelling path and the sphaleron and on which the energy functional is degenerate to second order in the fields. We prove that parts of this boundary coincide with the Gribov horizon with the help of bounds on the fundamental modular domain.Comment: 19p., 6 figs. appended in PostScript (uuencoded), preprint INLO-PUB-12/93. Revision: ONLY change is a much more economic PostScript code for figures 1-4 (with apologies

Nahm gauge fields for the torus

We present the exact expression for the Nahm gauge field associated to a SU(N) charge one self-dual gauge field on T^3XR. The result implies that the size of the instanton is determined by the ``distance'' between its two flat connections at t plus or minus infinty.Comment: 9 pages, late