Antisymplectic Gauge Theories

A general field-antifield BV formalism for antisymplectic first class constraints is proposed. It is as general as the corresponding symplectic BFV-BRST formulation and it is demonstrated to be consistent with a previously proposed formalism for antisymplectic second class constraints through a generalized conversion to corresponding first class constraints. Thereby the basic concept of gauge symmetry is extended to apply to quite a new class of gauge theories potentially possible to exist.Comment: 13 pages,Latexfile,New introductio

Gauge dependence in topological gauge theories

We parametrize the gauge-fixing freedom in choosing the Lagrangian of a topological gauge theory. We compute the gauge-fixing dependence of correlators of equivariant operators when the compactified moduli space has a non-empty boundary and verify that only a subset of these has a gauge independent meaning. We analyze in detail a simple example of such anomalous topological theories, 4D topological Yang-Mills on the four-sphere and instanton number k=1.Comment: 12 pages, TeX , harvma

Translational groups as generators of gauge transformations

We examine the gauge generating nature of the translational subgroup of Wigner's little group for the case of massless tensor gauge theories and show that the gauge transformations generated by the translational group is only a subset of the complete set of gauge transformations. We also show that, just like the case of topologically massive gauge theories, translational groups act as generators of gauge transformations in gauge theories obtained by extending massive gauge noninvariant theories by a Stuckelberg mechanism. The representations of the translational groups that generate gauge transformations in such Stuckelberg extended theories can be obtained by the method of dimensional descent. We illustrate these with the examples of Stuckelberg extended first class versions of Proca, Einstein-Pauli-Fierz and massive Kalb-Ramond theories in 3+1 dimensions. A detailed analysis of the partial gauge generation in massive and massless 2nd rank symmetric gauge theories is provided. The gauge transformations generated by translational group in 2-form gauge theories are shown to explicitly manifest the reducibility of gauge transformations in these theories.Comment: Latex, 20 pages, no figures, Version to appear in Physical Review

Lattice chiral gauge theories through gauge fixing

After an introduction in which we review the fundamental difficulty in constructing lattice chiral gauge theories, we discuss the analytic and numerical evidence that abelian lattice chiral gauge theories can be non-perturbatively constructed through the gauge-fixing approach. While a complete non-abelian extension is still under construction, we also show how fermion-number violating processes are realized in this approach.Comment: 12 pages; talk given at the ``Workshop on Confinement, Topology and other Non-perturbative Aspects of QCD,'' Stara Lesna (Slovakia), 21-27 Jan 200

Lattice Chiral Gauge Theories

I review the substantial progress which has been made recently with the non-perturbative construction of chiral gauge theories on the lattice. In particular, I discuss three different approaches: a gauge invariant method using fermions which satisfy the Ginsparg-Wilson relation, and two gauge non-invariant methods, one using different cutoffs for the fermions and the gauge fields, and one using gauge fixing. Open problems within all three approaches are addressed.Comment: 15 pages, 2 figs, Lattice 2000 (Plenary