Related papers: Quantization of soluble classical constrained syst…
In the Dirac bracket approach to dynamical systems with second class constraints observables are represented by elements of a quotient Dirac bracket algebra. We describe families of new realizations of this algebra through quotients of the…
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…
We provide a simultaneous derivation of the Dirac bracket and of the equations of motion for second-class constrained systems when the constraints are time-dependent. The necessity of time-dependent gauge-fixing conditions is shown in the…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…
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 Jacobi theta-functions admit a definition through the autonomous differential equations (dynamical system); not only through the famous Fourier theta-series. We study this system in the framework of Hamiltonian dynamics and find…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
We present two possible criteria quantifying the degree of classicality of an arbitrary (finite dimensional) dynamical system. The inputs for these criteria are the classical dynamical structure of the system together with the quantum and…
A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
Finding classical canonical observables consists of taking a function space over phase space. For constrained theories, these functions must form zero brackets with a closed algebraic structure of first-class constraints. This brackets…
Classical mechanics involves position and momentum variables that must be special coordinates chosen to promote to suitable quantum operators. Since classical variables may be broadly chosen, only unique variables should be chosen. We will…
Hydrodynamic turbulence is studied as a constrained system from the point of view of metafluid dynamics. We present a Lagrangian description for this new theory of turbulence inspired from the analogy with electromagnetism. Consequently it…
Quantization relates Poisson algebras to $C^*$-algebras. The analysis of local gauge symmetries in algebraic quantum field theory is approached through the quantization of classical gauge theories, regarded as constrained dynamical systems.…
We emphasize the usefulness of the Lie brackets in the context of classical and quantum mechanics. By way of examples we show that many dynamical systems, especially the ones with (gauge) constraints, can equally be treated in their time…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…