Related papers: Four approaches to quantization of the relativisti…
Recent results of BRST quantization on inner product spaces are reviewed. It is shown how relativistic particle models may be quantized with finite norms and that the relation between the operator method and the conventional path integral…
I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the…
We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
In my textbook on Quantum Field Theory \cite{tpqft} and in a recent paper \cite{tpejc2018}, I advocated a lattice regularization procedure for defining the path integral for the relativistic particle, using the non-quadratic action…
Recently derived general formal solutions of a BRST quantization on inner product spaces of irreducible Lie group gauge theories are applied to trivial models and relativistic particle models for particles with spin 0, 1/2 and 1. In the…
Usually the only difference between relativistic quantization and standard one is that the Lagrangian of the system under consideration should be Lorentz invariant. The standard approaches are logically incomplete and produce solutions with…
Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…
The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener…
For a particle moving in a one-dimensional space an under a periodic external force, its quantization is study using the Hamiltonian (generalized linear momentum quantization) and constant of motion (velocity quantization) approaches. it is…
Relativistic generalization of Path Integral Monte-Carlo method has been proposed and some possible applications have been discussed.
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
A phase space treatment of special relativity of quantum systems is developed. In this approach a quantum particle remains localized if subject to inertial transformations, the localization occurring in a finite phase space area. Unlike…
We study some features of bosonic particle path-integral quantization in a twistor-like approach by use of the BRST-BFV quantization prescription. In the course of the Hamiltonian analysis we observe links between various formulations of…
For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltoninan of this system. Thus, the quantization of this system is carried out…
We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing…
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…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
Using the BFV approach we quantize a pseudoclassical model of the spin one half relativistic particle that contains a single bosonic constraint, contrary to the usual locally supersymmetric models that display first and second class…