Related papers: Deformation quantization of constrained systems: a…
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.…
We first generalise the standard Wigner function to Dirac fermions in curved spacetimes. Secondly, we turn to the Moyal quantisation of systems with constraints. Gravity is used as an example.
The Weyl-Wigner-Moyal formalism for Dirac second class constrained systems has been proposed recently as the deformation quantization of Dirac bracket. In this paper, after a brief review of this formalism, it is applied to the case of the…
In this paper, we present a detailed review/analysis of the Dirac quantisation of Hamiltonian systems with constraints. To this end, we use, as a guide, the physical example provided by the dynamics of a solid ball rolling, without…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
The Dirac quantization `procedure' for constrained systems is well known to have many subtleties and ambiguities. Within this ill-defined framework, we explore the generality of a particular interpretation of the Dirac procedure known as…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
This work addresses certain ambiguities in the Dirac approach to constrained systems. Specifically, we investigate the space of so-called ``rigging maps'' associated with Refined Algebraic Quantization, a particular realization of the Dirac…
In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
We present a novel framework for quantizing constrained quantum systems in which the processes of quantization and constraint enforcement are performed simultaneously. The approach is based on an extension of the stationary action…
A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form…
When the gauge group of a theory has infinite volume, defining the inner product on physical states becomes subtle. This is the case for gravity, even in exactly solvable models such as minisuperspace or low-dimensional theories: the…
We apply a new and mathematically rigorous method for the quantization of constrained systems to two-dimensional gauge theories. In this method, which quantizes Marsden-Weinstein symplectic reduction, the inner product on the physical state…
A general quantum constraint of the form $C= - \partial_T^2 \otimes B - I\otimes H$ (realized in particular in Loop Quantum Cosmology models) is studied. Group Averaging is applied to define the Hilbert space of solutions and the relational…
We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution.…
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…
We propose an explicit construction of the deformation quantization of the general second-class constrained system, which is covariant with respect to local coordinates on the phase space. The approach is based on constructing the effective…
The ADM approach to canonical general relativity combined with Dirac's method of quantizing constrained systems leads to the Wheeler-DeWitt equation. A number of mathematical as well as physical difficulties that arise in connection with…
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…