Related papers: ALAG - quantization
This paper is a short version of the author habilitation thesis. The main results have been already published but here a lot of details are clarified. As well we add some new results: we discuss some quasi classical limit of ALG(a) -…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
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…
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),…
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…
A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do \textit{not} necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange…
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…
New features of a previously introduced Group Approach to Quantization are presented. We show that the construction of the symmetry group associated with the system to be quantized (the "quantizing group") does not require, in general, the…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
We perform a canonical, reduced phase space quantisation of General Relativity by Loop Quantum Gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the combination of 1. the Brown -- Kuchar…
In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not…
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…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
An algebraic quantization procedure for discretized spacetime models is suggested based on the duality between finitary substitutes and their incidence algebras. The provided limiting procedure that yields conventional manifold…
The physical variables of classical thermodynamics occur in conjugate pairs such as pressure/volume, entropy/temperature, chemical potential/particle number. Nevertheless, and unlike in classical mechanics, there are an odd number of such…
We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of simple but restrictive rules of the game lead to conditions for an isomorphism between…
Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel {\sigma}-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations.…
This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the moduli space of stable algebraic curves and,…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
We propose the new quantization of homogenous cosmological models. Four fundamental methods are applied to the cosmological model and efficiently jointed. The Dirac method for constrained systems is used, then the Fock space is built and…