Related papers: Fully extended BV-BFV description of General Relat…
We describe a canonical reduction of AKSZ-BV theories to the cohomology of the source manifold. We get a finite dimensional BV theory that describes the contribution of the zero modes to the full QFT. Integration can be defined and…
These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The…
We show how to derive asymptotic charges for field theories on manifolds with "asymptotic" boundary, using the BV-BFV formalism. We also prove that the conservation of said charges follows naturally from the vanishing of the BFV boundary…
In this paper, we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations.…
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…
We show in this paper that it is possible to formulate General Relativity in a phase space coordinatized by two $SO(3)$ connections. We analyze first the Husain-Kucha\v{r} model and find a two connection description for it. Introducing a…
The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein-Hilbert term with…
A generalized three-form field is an extended version of the canonical three-form field by considering a Lagrangian of the generalized three-form field as a function of the kinetic and the mass terms. In this work, we investigated…
First, let the fractal dimension D=n(integer)+d(decimal), so the fractal dimensional matrix was represented by a usual matrix adds a special decimal row (column). We researched that mathematics, for example, the fractal dimensional linear…
We study generalizations of 3- and 4-dimensional BF-theory in the context of higher gauge theory. First, we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of…
We propose a superfield formalism of Lagrangian BRST-antiBRST quantization of arbitrary gauge theories in general coordinates with the base manifold of fields and antifields desribed in terms of both bosonic and fermionic variables.
The Standard Model plus gravitation is derived from general relativity with three dimensions of time. I claim that when the Lagrangian for general relativity is calculated using three dimensions of time, the unified field theory results. I…
We study the action for the three-space formalism of General Relativity, better known as the BF\'O (Barbour--Foster--\'O Murchadha) action, which is a square-root BSW (Baierlein--Sharp--Wheeler) action. In particular, we explore the…
In this paper we consider an extended Gauss-Bonnet gravity theory in arbitrary dimensions and in a space provided with a Weyl connection, which is torsionless but not metric-compatible, the non-metricity tensor being determined by a vector…
We generalise a recent derivation of the relativistic expressions for momentum and kinetic energy from the one-dimensional to the three-dimensional case.
Three different methods to quantize the spherically symmetric sector of electromagnetism are presented: First, it is shown that this sector is equivalent to Abelian BF-theory in four spacetime dimensions with suitable boundary conditions.…
Working in the Palatini formalism, we describe a procedure for constructing degenerate solutions of general relativity on 4-manifold M from certain solutions of 2-dimensional BF theory on any framed surface Sigma embedded in M. In these…
We relate the notions of BB-tilting and perverse derived equivalence at a vertex. Based on these notions, we define mutations of algebras, leading to derived equivalent ones. We present applications to endomorphism algebras of…
We examine a unitarity of a particular higher-derivative extension of general relativity in three space-time dimensions, which has been recently shown to be equivalent to the Pauli-Fierz massive gravity at the linearized approximation…
Constrained hamiltonian structure of noncommutative gauge theory for the gauge group U(1) is discussed. Constraints are shown to be first class, although, they do not give an Abelian algebra in terms of Poisson brackets. The related…