Related papers: Reduced Phase Space Quantization and Dirac Observa…

We consider (2+1)-gravity with vanishing cosmological constant as a constrained dynamical system. By applying Dirac's gauge fixing procedure, we implement the constraints and determine the Dirac bracket on the gauge-invariant phase space.…

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…

We analyze the quantization of dynamical systems that do not involve any background notion of space and time. We give a set of conditions for the introduction of an intrinsic time in quantum mechanics. We show that these conditions are a…

We study the consequences of the modification of the phase space structure of General Relativity imposed by breaking the full diffeomorphism invariance but retaining the time foliation preserving diffeomorphisms. We examine the different…

Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet (UV) modifications of quantum theory due to gravity, this work shows that generic infrared (IR)…

Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…

The reduced basis method is used to construct a "universal" basis of Dirac orbitals that may be applicable throughout the nuclear chart to calibrate covariant energy density functionals. Relative to our earlier work using the…

The split involution quantization scheme, proposed previously for pure second--class constraints only, is extended to cover the case of the presence of irreducible first--class constraints. The explicit Sp(2)--symmetry property of the…

We show an equivalence between Dirac quantization and the reduced phase space quantization. The equivalence of the both quantization methods determines the operator ordering of the Hamiltonian. Some examples of the operator ordering are…

The $D$-dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. For D=3, it includes Snyder algebra as a special…

The Doplicher, Fredenhagen and Roberts (DFR) noncommutative (NC) formalism is propose in a curved space-time. In DFR approach, the NC parameter is promoted to the set of coordinates of the space-time. As consequence, the field theory…

We investigate refined algebraic quantisation of the constrained Hamiltonian system introduced by Boulware as a simplified version of the Ashtekar-Horowitz model. The dimension of the physical Hilbert space is finite and asymptotes in the…

Identifying an appropriate set of ``observables'' is a nontrivial task for most approaches to quantum gravity. We describe how it may be accomplished in the context of a recently proposed family of stochastic (but classical) dynamical laws…

Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system…

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.

We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not…

A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in…

This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…

The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…

This is a collection of lectures given at the University of Heidelberg, especially but not exclusively for people who want to learn something about the canonical approach to quantum gravity, which is however not included in these lectures.…