The factorisation of glue and mass terms in SU(N) gauge theories

In this paper we investigate the structure of the glue in Zwanziger's gauge invariant expansion for the A^2-type mass term in Yang-Mills theory. We show how to derive this expansion, in terms of the inverse covariant Laplacian, and extend it to higher orders. In particular, we give an explicit expression, for the first time, for the next to next to leading order term. We further show that the expansion is not unique and give examples of the resulting ambiguity.Comment: 22 page

On Nonexistence of Magnetic Charge in Pure Yang-Mills Theories

We prove that magnetic charge does not exist as a physical observable on the physical Hilbert space of the pure SU(2) gauge theory. The abelian magnetic monopoles seen in lattice simulations are then interpreted as artifacts of gauge fixing. The apparent physical scaling properties of the monopole density in the continuum limit observed on the lattice are attributed to the correct scaling properties of physical objects - magnetic vortices, as first argued by Greensite et. al. We can show that a local gauge transformation of a certain type can " create" abelian monopole-antimonopole pairs along magnetic vortices. This gauge transformation exists in pure SU(N) gauge theory at any $N$.Comment: Some references and comments adde

Infra-Red Finite Charge Propagation

The Coulomb gauge has a long history and many uses. It is especially useful in bound state applications. An important feature of this gauge is that the matter fields have an infra-red finite propagator in an on-shell renormalisation scheme. This is, however, only the case if the renormalisation point is chosen to be the static point on the mass shell, p = (m, 0, 0, 0). In this letter we show how to extend this key property of the Coulomb gauge to an arbitrary relativistic renormalisation point. This is achieved through the introduction of a new class of gauges of which the Coulomb gauge is a limiting case. A physical explanation for this result is given.Comment: 8 pages, plain TeX, to appear in Modern Physics Letters

Hodge Duality Operation And Its Physical Applications On Supermanifolds

An appropriate definition of the Hodge duality $\star$ operation on any arbitrary dimensional supermanifold has been a long-standing problem. We define a working rule for the Hodge duality $\star$ operation on the $(2 + 2)$-dimensional supermanifold parametrized by a couple of even (bosonic) spacetime variables $x^\mu (\mu = 0, 1)$ and a couple of Grassmannian (odd) variables $\theta$ and $\bar\theta$ of the Grassmann algebra. The Minkowski spacetime manifold, hidden in the supermanifold and parametrized by $x^\mu (\mu = 0, 1)$, is chosen to be a flat manifold on which a two $(1 + 1)$-dimensional (2D) free Abelian gauge theory, taken as a prototype field theoretical model, is defined. We demonstrate the applications of the above definition (and its further generalization) for the discussion of the (anti-)co-BRST symmetries that exist for the field theoretical models of 2D- (and 4D) free Abelian gauge theories considered on the four $(2 + 2)$- (and six $(4 + 2)$)-dimensional supermanifolds, respectively.Comment: LaTeX file, 25 pages, Journal-versio