Related papers: Can We Look at The Quantisation Rules as Constrain…

We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The…

The Moyal quantization is described as a discretization of the classical phase space by using difference analogue of vector fields. Difference analogue of Lie brackets plays the role of Heisenberg commutators.

Lately, to provide a solid ground for quantization of the open string theory with a constant B-field, it has been proposed to treat the boundary conditions as hamiltonian constraints. It seems that this proposal is quite general and should…

We combine the "evolving constants" approach to the construction of observables in canonical quantum gravity with the Page--Wootters formulation of quantum mechanics with a relational time for generally covariant systems. This overcomes the…

We argue that the field-parametrization dependence of Dirac's procedure, for Hamiltonians with first-class constraints not only preserves covariance in covariant theories, but in non-covariant gauge theories it allows one to find the…

Phase space of General Relativity is extended to a Poisson manifold by inclusion of the determinant of the metric and conjugate momentum as additional independent variables. As a result, the action and the constraints take a polynomial…

In this paper, we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity to the Poisson structure for non-dissipative systems. We develop a canonical description for…

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…

We apply the reduced phase space quantization to the Kasner universe. We construct the kinematical phase space, find solutions to the Hamilton equations of motion, identify Dirac observables and arrive at physical solutions in terms of…

We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components…

Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…

When we have noncommutativity among coordinates (or conjugate momenta), we consider Wigner's formulation of quantum mechanics, including a new derivation of path integral formula. We also propose the Moyal star product based on the Dirac…

We investigate the Hubbard model in the limit $U=\infty$, which is equivalent to the statistical condition of exclusion of double occupancy. We solve this problem using Dirac's method for constraints. The constraints are solved within the…

The concept of a Dirac algebroid, which is a linear almost Dirac structure on a vector bundle, was designed to generate phase equations for mechanical systems with linear nonholonomic constraints. We apply it to systems with magnetic-like…

The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets…

In this work we study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these spaces as fundamental Dirac brackets,…

We investigate using plane fronted gravitational wave space-times as model systems to study loop quantization techniques and dispersion relations. In this classical analysis, we start with planar symmetric space-times in the real connection…

The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields…

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…

A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit…