Coordinate-free quantization of first-class constrained systems

The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough to include Yang-Mills type theories with an arbitrary compact gauge group. Central to this extension are the use of coherent state path integrals and of Lagrange multiplier integrations that engender projection operators onto the subspace of gauge invariant states

Phase space structure and the path integral for gauge theories on a cylinder

The physical phase space of gauge field theories on a cylindrical spacetime with an arbitrary compact simple gauge group is shown to be the quotient ${\bf R}^{2r}/W_A,$ $r$ a rank of the gauge group, $W_A$ the affine Weyl group. The PI formula resulting from Dirac's operator method contains a symmetrization with respect to $W_A$ rather than the integration domain reduction. It gives a natural solution to Gribov's problem. Some features of fermion quantum dynamics caused by the nontrivial phase space geometry are briefly discussed.Comment: Saclay-T93/07

Dynamical Abelian Projection of Gluodynamics

Assuming the monopole dominance, that has been proved in the lattice gluodynamics, to hold in the continuum limit, we develop an effective scalar field theory for QCD at large distances to describe confinement. The approach is based on a gauge (or projection) independent formulation of the monopole dominance and manifestly Lorentz invariant.Comment: A talk given at QCD96, Montpellier, France, July, 1996 (to appear in the Proceedings); plain Latex, 6 page

Infrared Yang-Mills theory as a spin system. A lattice approach

To verify the conjecture that Yang-Mills theory in the infrared limit is equivalent to a spin system whose excitations are knot solitons, a numerical algorithm based on the inverse Monte Carlo method is proposed. To investigate the stability of the effective spin field action, numerical studies of the renormalization group flow for the coupling constants are suggested. A universality of the effective spin field action is also discussed.Comment: Latex 12 pages, no figures, references added, some comments added, to appear in Phys.Lett.