A Study of Gaugeon Formalism for QED in Lorentz Violating Background

At the energy regimes close to Planck scales, the usual structure of Lorentz symmetry fails to address certain fundamental issues and eventually breaks down, thus paving the way for an alternative road map. It is thus argued that some subgroup of proper Lorentz group could stand consistent and might possibly help us to circumvent this problem.It is this subgroup that goes by the name of Very Special Relativity(VSR). Apart from violating rotational symmetry,VSR is believed to preserve the very tenets of special relativity. The gaugeon formalism due to type-I Yokoyama and type-II Izawa are found to be invariant under BRST symmetry. In this paper, we analyze the scope of this invariance in the scheme of VSR. Furthermore, we will obtain VSR modified Lagrangian density using path integral derivation. We will explore the consistency of VSR with regard to these theories.     

General Formalism for the BRST Symmetry

In this paper we will discuss Faddeev-Popov method for gauge theories with a general form of gauge symmetry in an abstract way. We will then develope a general formalism for dealing with the BRST symmetry. This formalism will make it possible to analyse the BRST symmetry for any theory.     

No cross‐interactions between the Weyl graviton and the massless Rarita‐Schwinger field

The proof of the fact that there are no nontrivial, consistent cross‐couplings that can be added between the Weyl graviton and the massless Rarita‐Schwinger field is accomplished by means of a cohomological approach, based on the deformation of the solution to the master equation from the antifield‐Becchi‐Rouet‐Stora‐Tyutin (BRST) formalism. The procedure developed here relies on the assumptions of locality, smoothness, (background) Lorentz invariance, Poincaré invariance, and preservation of the number of derivatives with respect to each field (the last hypothesis was made only in antighost number zero).     

BRST invariance and the conical pendulum

The Hamiltonian formulation of the BRST method for quantizing constrained systems developed recently by Nemeschanskyet al is applied to the well-known problem of the conical pendulum in classical mechanics. The similarity of the system to a gauge theory wherein the two constraints serve as generators of local Abelian gauge transformations is also pointed out. The definition of the physical states of the system as a gauge theory and also as a BRST invariant theory is then discussed in some detail.     

Cohomological derivation of the couplings between an abelian gauge field and matter fields

Consistent couplings between an abelian gauge field and a system of matter fields are investigated by means of Lagrangian cohomological arguments.     

A superspace path integral proof of the Gauss-Bonnet-Chern theorem

A rigorous theory of integration in the space of paths in super space is developed, by extending Berezin's method of integration to spaces of anticommuting variables with an uncountably high dimension. A Feynmam-Kac-Ito formula for the heat kernel of a wide class of superspace differential operators is established. This formula is then used to make rigorous the supersummetric proofs of the Gauss-Bonnet-Chern theorem [1, 2].     

On the connection between Pauli-Villars and higher derivative regularizations

We show that in some cases the gauge-invariant Pauli-Villars and higher (covariant) derivative regularizations are equivalent.     

The Quantum Formalism and the GRW Formalism

The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something that has until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRWm or GRWf world.     

The GHP Formalism and a Type N Twisting Vacuum Metric with Killing Vector

It is shown that the formalism introduced byGeroch, Held and Penrose has a geometrical basis. Withthe help of the resulting insight a canonical splittingof the complex function which appears in the standard form of the Algebraically Special metrics isrealized. The results of this splitting are applied tothe problem of a (special) Type N vacuum metric with atwisting principle null direction. It is demonstrated that it is possible (but not feasable) to findthe metric without the use of differential equations. Anestimate of the size of the metric is given.     

BRST invariance in Coulomb gauge QCD

In the Coulomb gauge, the Hamiltonian of QCD contains terms of order ?²${?}^2$, identified by Christ and Lee, which are non-local but instantaneous. The question is addressed how do these terms fit in with BRST invariance. Our discussion is confined to the simplest, O(g⁴)$O\left(g^4\right)$, example.     

Short Representations of SU(2,2/N) and Harmonic Superspace Analyticity

We consider the harmonic superspaces associated with SU(2,2/N) superconformal algebras. For arbitrary N, we show that massless representations, other than the chiral ones, correspond to [N/2] elementary ultrashort analytic superfields whose first component is a scalar in the k antisymmetric irrep of SU(N) (k=1...[N/2]) with top spin J _top=(N/2–k/2,0). For N=2n, we analyze UIR's obtained by tensoring the self-conjugate ultrashort multiplet J _top=(n/2,0) and show that N–1 different basic products give rise to all possible UIR's with residual shortening.     

Finite field-dependent symmetries in perturbative quantum gravity

In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation.     

The BV Formalization of Chern-Simons Theory on Deformed Superspace

In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-Simons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky (BV) formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.     

Integration in the GHP Formalism II: An Operator Approach for Spacetimes with Killing Vectors, with Applications to Twisting Type N Spaces

Held has proposed a coordinate- and gauge-free integration procedure within the ghp formalism built around four functionally independent zero-weighted scalars constructed from the spin coefficients and the Riemann tensor components. Unfortunately, a spacetime with Killing vectors (and hence cyclic coordinates in the metric, and in all quantities constructed from the metric) may be unable to supply the full quota of four scalars of this type. However, for such a spacetime additional scalars may be supplied by the components of the Killing vectors. As an illustration we investigate the vacuum type N spaces admitting a Killing vector and a homothetic Killing vector. In a direct manner, we reduce the problem to a pair of ordinary differential operator master equations, making use of a new zero-weighted ghp operator. In two different ways, we show how these master equations can be reduced to one real third-order operator differential equation for a complex function of a real variable—but still with the freedom to choose explicitly our fourth coordinate. It is then easy to see there is a whole class of coordinate choices where the problem reduces essentially to one real third-order differential equation for a real function of a real variable. It is also outlined how the various other differential equations, which have been derived previously in work on this problem, can be deduced from our master equations.     

Computation of the chiral anomaly in the bulk quantization

The bulk quantization method is used for regularizing a conventional four dimensional theory of massless fermions coupled to an external non‐Abelian gauge field and for subsequently evaluating the associated Ward identity. As a result one obtains the well‐known chiral anomaly.     

The d = [δ, b] Decomposition of Topological Yang–Mills Theory

We review the construction of topological Yang–Mills theory (TYMT) from the point of view of an operator satisfying d = [, b] with b the BRST operator. We focus our attention on a situation in which [, d] 0 and show how this leads us to consider a more general derivative ~d = b + d + _{k 2 k} ^1–k .     

BRST Extension of Geometric Quantization

Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically rigorous BRST quantization of the constrained system whose cohomology at ghost number zero recovers the constrained quantum states. Moreover this space of constrained states has a well-defined Hilbert space structure inherited from that of the original system. Treatments of these ideas in the physics literature are more general but suffer from having states with infinite or zero "norms" and thus are not admissible as states. Also BRST operators for many systems require regularization to be well-defined. In our more restricted context, we show that our treatment does not suffer from any of these difficulties.