Some Observations on Non-covariant Gauges and the epsilon-term

We consider the Lagrangian path-integrals in Minkowski space for gauges with a residual gauge-invariance. From rather elementary considerations, we demonstrate the necessity of inclusion of an epsilon-term (even) in the formal treatments, without which one may reach incorrect conclusions. We show, further, that the epsilon-term can contribute to the BRST WT-identities in a nontrivial way (even as epsilon-->0). We also show that the (expectation value of the) correct epsilon-term satisfies an algebraic condition. We show by considering (a commonly used) example of a simple local quadratic epsilon -term, that they lead to additional constraints on Green's function that are not normally taken into account in the BRST formalism that ignores the epsilon-term, and that they are characteristic of the way the singularities in propagators are handled. We argue that for a subclass of these gauges, the Minkowski path-integral could not be obtained by a Wick rotation from a Euclidean path-integral.Comment: 12 pages, LaTeX2

Absence of Nonlocal Counter-terms in the Gauge Boson Propagator in Axial -type Gauges

We study the two-point function for the gauge boson in the axial-type gauges. We use the exact treatment of the axial gauges recently proposed that is intrinsically compatible with the Lorentz type gauges in the path-integral formulation and has been arrived at from this connection and which is a ``one-vector'' treatment. We find that in this treatment, we can evaluate the two-point functions without imposing any additional interpretation on the axial gauge 1/(n.q)^p-type poles. The calculations are as easy as the other treatments based on other known prescriptions. Unlike the ``uniform-prescription'' /L-M prescription, we note, here, the absence of any non-local divergences in the 2-point proper vertex. We correlate our calculation with that for the Cauchy Principal Value prescription and find from this comparison that the 2-point proper vertex differs from the CPV calculation only by finite terms. For simplicity of treatment, the divergences have been calculated here with n^2>0 and these have a smooth light cone limit.Comment: 17 pages; 3 figures drawn using feyn.st

Relating Green's Functions in Axial and Lorentz Gauges using Finite Field-Dependent BRS Transformations

We use finite field-dependent BRS transformations (FFBRS) to connect the Green functions in a set of two otherwise unrelated gauge choices. We choose the Lorentz and the axial gauges as examples. We show how the Green functions in axial gauge can be written as a series in terms of those in Lorentz gauges. Our method also applies to operator Green's functions. We show that this process involves another set of related FFBRS transfomations that is derivable from infinitesimal FBRS. We suggest possible applications.Comment: 20 pages, LaTex, Section 4 expanded, typos corrected; last 2 references modified; (this) revised version to appear in J. Math. Phy

Possible Detection of Causality Violation in a Non-local Scalar Model

We consider the possibility that there may be causality violation detectable at higher energies. We take a scalar nonlocal theory containing a mass scale $\Lambda$ as a model example and make a preliminary study of how the causality violation can be observed. We show how to formulate an observable whose detection would signal causality violation. We study the range of energies (relative to $\Lambda$) and couplings to which the observable can be used.Comment: Latex, 30 page

A superspace formulation of Abelian antisymmetric tensor gauge theory

We apply a superspace formulation to the four-dimensional gauge theory of a massless Abelian antisymmetric tensor field of rank 2. The theory is formulated in a six-dimensional superspace using rank-2 tensor, vector and scalar superfields and their associated supersources. It is shown that BRS transformation rules of fields are realized as Euler-Lagrange equations without assuming the so-called horizontality condition and that a generating functional $\bar{W}$ constracted in the superspace reduces to that for the ordinary gauge theory of Abelian rank-2 antisymmetric tensor field. The WT identity for this theory is derived by making use of the superspace formulation and is expressed in a neat and compact form $\partial\bar{W}/\partial\theta=0$.Comment: Latex, 19pages, No fig

Relating the generating functionals in field/antifield formulation through finite field dependent BRST transformation

We study the field/antifield formulation of pure Yang Mills theory in the framework of finite field dependent BRST transformation. We show that the generating functionals corresponding to different solutions of quantum master equation are connected through the finite field dependent BRST transformations. We establish this result with the help of several explicit examples.Comment: Revtex4, 18 pages, No figs, Accepted in Eur. Phys. J

Superspace Formulation of Yang- Mills Theory II: Inclusion of Gauge Invariant Operators and Scalars

In a superspace formulation of Yang-Mills theory previously proposed, we show how gauge-invariant operators and scalars can be incorporated keeping intact the (broken) $Osp(3,1|2)$ symmetry of the superspace action. We show in both cases, that the WT identities can be cast in a simple form $\frac{\partial\bar{W}}{\partial\theta}=0$.Comment: Revtex, 19 pages, No figure