Related papers: A pure Dirac's method for Husain-Kuchar theory
Canonical quantization entails using Cartesian coordinates, and Cartesian coordinates exist only in flat spaces. This situation can either be questioned or accepted. In this paper we offer a brief and introductory overview of how a flat…
We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges…
We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as…
The present article is primarily a review of the projection-operator approach to quantize systems with constraints. We study the quantization of systems with general first- and second-class constraints from the point of view of…
The model of a classical particle with the weak linear AAD potential is subjected to path integral quantization. The light cone constraints and peculiar properies of its internal variables permit to use in calculations commutative dynamics…
Canonical quantization of gravitational systems is obstructed by the problem of time. Due to diffeomorphism symmetry the Hamiltonian vanishes: dynamics with respect to a background time parameter appears "frozen." Two strategies towards the…
We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in $D$ dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first…
We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact…
A generalization of the Dirac's canonical quantization theory for a system with second-class constraints is proposed as the fundamental commutation relations that are constituted by all commutators between positions, momenta and Hamiltonian…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Building towards a more covariant approach to canonical classical and quantum gravity we outline an approach to constrained dynamics that de-emphasizes the role of the Hamiltonian phase space and highlights the role of the Lagrangian phase…
Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (``simplicity'' constraints). Within this framework, we underline a…
A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously…
We suggest to use "minimal" choice of quantum gravity theory, that is the quantum field theory, in which space-time is seen as Riemannian space and metric (or vierbein field) is the dynamical variable. We then suggest to use the simplest…
The method for quantization of constrained theories that was suggested originally by Faddeev and Jackiw along with later modifications is discussed. The particular emphasis of this paper is to show how it is simple to implement their method…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
We investigate a minisuperspace model of Einstein gravity plus dilaton that describes a static spherically symmetric configuration or a Kantowski - Sachs like universe. We develop the canonical formalism and identify canonical quantities…
We study the Dirac equation minimally coupled to general relativity using quantum field theory and the semiclassical gravity approximation. Previous studies of the Einstein-Dirac system did not quantize the Dirac field and required multiple…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
A pure Dirac's framework for 3D Palatini's theory with cosmological constant is performed. By considering the complete phase space, we find out the full structure of the constraints, and their corresponding algebra is computed explicitly.…