We point out missing links in the recent paper by Tomboulis in which he claims a rigorous proof of quark confinement in 4D lattice gauge theory. We also discuss if it is possible to correct his proof.

Let g be a diametric gauge over a metric space (X, p). It is proved, in this paper, that the upper gauge density D (A, x) = 0 for almost all points of the complement of A provided that A is in a certain family which contains all Borel sets of finite measure. Also, a relation between conditions for a diametric gauge and certain regularity conditions is given.

We establish the ultraviolet finiteness of various classes of noncommutative gauge theories.

Superparticle actions in (10,2) and (11,3) dimensions are constructed. These actions have bosonic and fermionic gauge symmetries, and global target space supersymmety that generalize the reparametriza-tion, κ-symmetry and Poincaré supersymmetry of the usual superparticle. All these symmetries are realized in the phase space of two or three superparticles in (10,2) and (11,3) dimensions, respect...

We present results from magnetic monopoles in SU (2) lattice gauge theory at finite temperature. The lattices are 16 3 × N t , for N t = 4, 6, 8, 12, at β = 2.5115. Quantities discussed are: the spacial string tension, Polyakov loops, and the screening of timelike and spacelike magnetic currents.

We present preliminary data on the gluon propagator in generalized covariant gauges. The motivation for considering a generalized gauge-fixing procedure stems, just as in the continuum, from the necessity of studying the gauge dependence of the Green’s functions. In the covariant gauges it is possible to change the gauge fixing varying the value of the gauge parameter. In the continuum, the gen...

We show that a large class of Euclidean extended supersymmetric lattice gauge theories constructed in [1–3] can be regarded as compact formulations by using the polar decomposition of the complex link fields. In particular, the gauge part of the supersymmetric lattice action is the standard Wilson action. This formulation facilitates the construction of gauge invariant operators.

Using lattice simulations of a one-component (λΦ 4) 4 theory, we have measured the energy spectrum ω(k) in the broken phase at various lattice sizes. Our data show that the energy-gap ω(0) is not the 'Higgs mass' M h but an infrared-sensitive quantity that, conceivably, vanishes in the infinite-volume limit.