Emergence of the Haar measure in the standard functional integral representation of the Yang-Mills partition function

The conventional path integral expression for the Yang-Mills transition amplitude with flat measure and gauge-fixing built in via the Faddeev-Popov method has been claimed to fall short of guaranteeing gauge invariance in the non-perturbative regime. We show, however, that it yields the gauge invariant partition function where the projection onto gauge invariant wave functions is explicitly performed by integrating over the compact gauge group. In a variant of maximal Abelian gauge the Haar measure arises in the conventional Yang-Mills path integral from the Faddeev-Popov determinant.Comment: 14 pages, LaTeX, no figure

Magnetic Monopoles and the Topology of Gauge Fields

Lattice calculations performed in Abelian gauges give strong evidence that confinement is realized as a dual Meissner effect, implying that the Yang--Mills vacuum consists of a condensate of magnetic monopoles. We show in Polyakov gauge how the Pontrjagin index of the gauge field is related to the magnetic monopole charges.Comment: 4 pages, uses unicrc.sty and bbm.sty (included). Talk presented at the Int. Conf. QCD--98, Montpellier, July 199

Center vortex model for the infrared sector of Yang-Mills theory - Confinement and Deconfinement

A model for the infrared sector of Yang-Mills theory based on magnetic vortices represented by (closed) random surfaces is investigated using lattice Monte Carlo methods. The random surfaces are governed by a surface area action and a curvature action. The model generates a finite-temperature deconfinement transition; the coupling constants of the model can be chosen such as to reproduce the SU(2) Yang-Mills ratio of the deconfinement temperature to the square root of the zero-temperature string tension, T_c / sqrt{sigma_0} =0.69. This yields a physical trajectory in the space of coupling constants on which the confinement properties are approximately invariant. An at first sight surprisingly accurate prediction of the spatial string tension in the deconfined phase results, which can be made plausible in view of the specific space-time structure of the vortex configurations in this phase. The confinement properties are shown to be intimately tied to the percolation properties of the vortex surfaces.Comment: 16 pages, 7 ps figures included via epsf; revised version explores significantly enlarged range of coupling constants, conclusions unchanged, some references adde

On the Yang-Mills wave functional in Coulomb gauge

We investigate the dependence of the Yang-Mills wave functional in Coulomb gauge on the Faddeev-Popov determinant. We use a Gaussian wave functional multiplied by an arbitrary power of the Faddeev-Popov determinant. We show, that within the resummation of one-loop diagrams the stationary vacuum energy is independent of the power of the Faddeev-Popov determinant and, furthermore, the wave functional becomes field-independent in the infrared, describing a stochastic vacuum. Our investigations show, that the infrared limit is rather robust against details of the variational ans\"atze for the Yang-Mills wave functional. The infrared limit is exclusively determined by the divergence of the Faddeev-Popov determinant at the Gribov horizon.Comment: 9 pages, no figure