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In this paper the novel features of Yokoyama gaugeon formalism are stressed out for the theory of perturbative quantum gravity in Einstein curved spacetime. The quantum gauge transformations for the theory of perturbative gravity are…
The BRST-anti-BRST covariant extension is suggested for the split involution quantization scheme for the second class constrained theories. The constraint algebra generating equations involve on equal footing a pair of BRST charges for…
As a detailed application of the BV-BFV formalism for the quantization of field theories on manifolds with boundary, this note describes a quantization of the relational symplectic groupoid for a constant Poisson structure. The presence of…
We show that the associative algebra structure can be incorporated in the BRST quantization formalism for gauge theories such that extension from the corresponding Lie algebra to the associative algebra is achieved using operator…
This is a survey of our program of perturbative quantization of gauge theories on manifolds with boundary compatible with cutting/pasting and with gauge symmetry treated by means of a cohomological resolution (Batalin-Vilkovisky) formalism.…
The Becci-Rouet-Stora-Tyutin (BRST) operator quantization of a finite-dimensional gauge system featuring two quadratic super Hamiltonian and m linear supermomentum constraints is studied as a model for quantizing generally covariant gauge…
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit…
We introduce and study a new discrete basis of gravity constraints by making use of harmonic expansion for closed cosmological models. The full set of constraints is splitted into area-preserving spatial diffeomorphisms, forming closed…
We present BRST gauge fixing approach to quantum mechanics in phase space. The theory is obtained by $\hbar$-deformation of the cohomological classical mechanics described by d=1, N=2 model. We use the extended phase space supplied by the…
BFV--BRST charge for q-deformed algebras is not unique. Different constructions of it in the classical as well as in the quantum phase space for the $q$-deformed algebra sl_q(2) are discussed. Moreover, deformation of the phase space…
We exploit the 't Hooft-Polyakov monopole to define closed algebra of the quantum field operators and the BRST charge $Q_{BRST}$. In the first-class configuration of the Dirac quantization, by including the $Q_{BRST}$-exact gauge fixing…
We review the BV formalism in the context of $0$-dimensional gauge theories. For a gauge theory $(X_{0}, S_{0})$ with an affine configuration space $X_{0}$, we describe an algorithm to construct a corresponding extended theory $(\tilde{X},…
The BRST generator is realized as a Hermitian nilpotent operator for a finite-dimensional gauge system featuring a quadratic super-Hamiltonian and linear supermomentum constraints. As a result, the emerging ordering for the Hamiltonian…
We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincar\'e duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that…
In this paper we analyse a certain type of higher derivative gauge theories which are known to possess BRST symmetry associated with their higher derivative structure. We first show that these theories are also invariant under a anti-BRST…
Costello and Gwilliam have given both 1) a general definition of perturbative quantum gauge theory on a manifold M and 2) a construction of a factorization algebra of quantum observables assigned to every quantum gauge theory. In this…
This is the first in a series of papers on an attempt to understand quantum field theory mathematically. In this paper we shall introduce and study BV QFT algebra and BV QFT as the proto-algebraic model of quantum field theory by exploiting…
We analyze the quantum ABJM theory on ${\cal N} = 1$ superspace in different gauges. We study the Batalin-Vilkovisky (BV) formulation for this model. By developing field/antifield dependent BRST transformation we establish connection…
In this work, we propose a cohomological approach to studying perturbative anomalies in quantum mechanics. The Hamiltonian $\hat{H}$ together with the symmetry generator $\hat{S}$ forms a unitary representation of the two-dimensional…
Nonsingularity conditions are established for the BFV gauge-fixing fermion which are sufficient for it to lead to the correct path integral for a theory with constraints canonically quantized in the BFV approach. The conditions ensure that…