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

A superspace formulation of an "asymptotic" OSp(3,1|2) invariance of Yang-Mills theories

We formulate a superspace field theory which is shown to be equivalent to the $c-\bar{c}$ symmetric BRS/Anti-BRS invariant Yang-Mills action. The theory uses a 6-dimensional superspace and one OSp(3,1|2) vector multiplet of unconstrained superfields. We establish a superspace WT identity and show that the formulation has an asymptotic OSp(3,1|2) invariance as the gauge parameter goes to infinity. We give a physical interpretation of this asymptotic OSp(3,1|2) invariance as a symmetry transformation among the longitudinal/time like degrees of freedom of $A_\mu$ and the ghost degrees of freedom.Comment: Latex, 20pages, No fig

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

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

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

WT identities for proper vertices and renormalization in a superspace formulation of gauge theories

We formulate the WT identity for proper vertices in a simple and compact form $\partial \Gamma / {\partial \theta } =0$ in a superspace formulation of gauge theories proposed earlier. We show this WT identity (together with a subsidiary constraint) lead, in transparent way, the superfield superspace multiplet renormalizations formulated earlier (and shown to explain symmetries of Yang-Mills theory renormalization).Comment: 18 pages, Latex , Revised version, Appeared in PRD 5

Relating Calculations and Renormalization in Axial and Lorentz Gauges and Gauge-independence

We study futher the recently developed formalism for the axial gauges toward the comparison of calculations and of the renormalization procedure in the axial and the Lorentz gauges. We do this in the 1-loop approximation for the wavefunction renormalization and the identity of the beta-functions in the two gauges. We take as the starting point the relation between the Green's functions in the two gauges obtained earlier. We obtain the relation between the 1-loop propagators in the two gauges and locate those diagrams that contribute to the difference between the wave-function renormalizations in the two gauges. We further employ this relation between the Green's functions to the case of the 3-point function and prove the identity of the beta functions in the two gauges.Comment: 20 pages, 2 figues, Latex2

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