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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 generalized Einstein action is treated quantum mechanically by using a quadratic lagrangian form. The canonical quantization of this action is obtained by using the auxiliary variable to define the generalized momentum. Physical…
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…
We perform the canonical quantization of a relativistic spinless particle moving in a curved and static spacetime. We show that the classical theory already describes at the same time both particle and antiparticle. The analyses involves…
A detailed canonical treatment of a new action for a nonrelativistic particle coupled to background gravity, recently given by us, is performed both in the Lagrangian and Hamiltonian formulations. The equation of motion is shown to satisfy…
We study a class of noncanonical real scalar field models in $(1+1)$-dimensional flat space-time. We first derive the general criterion for the classical linear stability of an arbitrary static soliton solution of these models. Then we…
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…
Using canonical quantisation, and eschewing the Schwinger-Keldysh path integral, we derive a version of the Worldline Quantum Field Theory (WQFT) formalism suitable for both scattering and bound configurations of the classical two-body…
We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of…
The canonical quantization of the topological particle is described; it is shown that BRST quantization of the model gives the supersymmetric quantum mechanical model considered by Witten when investigating Morse theory, and the rigorous…
The canonical method of constrained system is discussed. The equations of motion for a free relativistic spinning particle are obtained without using gauge fixing conditions. The quantization of this model is discussed.
The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced…
Canonical formulation for an action containing scalar curvature squared term $(R^2)$ in arbitrary dimension has been performed in maximally symmetric space-time. The quantum dynamics does not alter significantly from the same in…
We study the properties of a relativistic model with logarithmic nonlinearity. We show that such model allows two types of solutions: topologically trivial (gaussons) and topologically non-trivial (kinks), depending on a sign of the…
Recently a linearized perturbation theory has been formulated for soliton sectors of quantum field theories. While it is more economical than alternative formalisms, such as collective coordinates, it is currently limited to solitons which…
We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions. Starting from the usual point particle action in the first order formalism, we introduce auxiliary variables which make the action locally…
We present, in the framework of the canonical quantization, a class of nonlinear Schroedinger equations with a complex nonlinearity describing, in the mean field approximation, systems of collectively interacting particles. The quantum…
We study the quantization of a classical system of interacting particles obeying a recently proposed kinetic interaction principle (KIP) [G. Kaniadakis, Physica A {\bf 296}, 405 (2001)]. The KIP fixes the expression of the Fokker-Planck…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
A consistent procedure of canonical quantization of pseudoclassical model for spin one relativistic particle is considered. Two approaches to treat the quantization for the massless case are discussed, the limit of the massive case and…