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A geometric prequantization formula for the Poisson-Gerstenhaber bracket of forms found within the DeDonder-Weyl Hamiltonian formalism earlier is presented. The related aspects of covariant geometric quantization of field theories are…
The purpose of this paper is to propose the implementation of some methods from algebraic geometry in the theory of gravitation, and more especially in the variational formalism. It has been assumed that the metric tensor depends on two…
A nonlinear Wightman field is taken to be a nonlinear map from a linear space of test functions to a linear space of Hilbert space operators, with inessential modifications to other axioms only to the extent dictated by the introduction of…
We discuss the problems of dynamics of the gravitational field and try to solve them according to quantum field theory by suggesting canonical states for the gravitational field and its conjugate field. To solve the problem of quantization…
In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field. The field strength of gravitational gauge field has both gravitational electric component and gravitational magnetic component. In…
We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we…
The negativity of the Wigner function is discussed as a measure of the non classicality and the quantum interference pattern obtained therein as a possible measure of the entanglement between the two modes of the vortex states. This measure…
In this article, we develop a formalism which is different from the standard lensing scenario and is necessary for understanding lensing by gravitational fields which arise as solutions of the effective Einstein equations on the brane. We…
From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in the former version, we analyze the vector and tensor…
We reorganize the derivative expansion of general (power-counting non-renormalizable) 2d dilaton gravity such that the mass function is integrable. As an example, we consider a three-parameter family of models and provide conditions on the…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of…
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted…
The multilevel geometrically--covariant generalization of the field--antifield BV--formalism is suggested. The structure of quantum generating equations and hypergauge conditions is studied in details. The multilevel formalism is…
We construct dual formulation of linearised gravity in first order tetrad formalism in arbitrary dimensions within the path integral framework following the standard duality algorithm making use of the global shift symmetry of the tetrad…
This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained which includes derivatives of the curvature. We analyze the form of the second field…
In various background independent approaches, quantum gravity is defined in terms of a field propagation kernel: a sum over paths interpreted as a transition amplitude between 3-geometries, expected to project quantum states of the geometry…
A new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and…
Light-cone quantization of gauge field theory is considered. With a careful treatment of the relevant degrees of freedom and where they must be initialized, the results obtained in equal-time quantization are recovered, in particular the…
In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hbar$ is proportional to the Dirac bracket.…