Related papers: Path integral for minisuperspaces and its relation…

Attempts to find a quantum-to-classical correspondence in a classically forbidden region leads to non-physical paths, involving, for example, complex time or spatial coordinates. Here, we identify genuine quasi-classical paths for tunneling…

I investigate the relationship between the phase space path integral in (2+1)-dimensional gravity and the canonical quantization of the corresponding reduced phase space in the York time slicing. I demonstrate the equivalence of these two…

For sufficiently tame paths in $\mathbb{R}^n$, Euclidean length provides a canonical parametrization of a path by length. In this paper we provide such a parametrization for all continuous paths. This parametrization is based on an…

The path integral representation for a system of N non-relativistic particles on the plane, interacting through a Chern-Simons gauge field, is obtained from the operator formalism. An effective interaction between the particles appears,…

In this paper, we review a method for computing and parameterizing the set of homotopy classes of chain maps between two chain complexes. This is then applied to finding topologically meaningful maps between simplicial complexes, which in…

On the basis of the canonical quantization procedure of a system defined on a cubic lattice, we propose a new method, in which resolutions of unity expressed in terms of eigenvectors are naturally provided, to find eigenvectors of field…

An interference experiment with entangled particles is theoretically analyzed, where one of the entangled pair (particle 1) goes through a multi-slit before being detected at a fixed detector. In addition, one introduces a mechanism for…

Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it…

For the case of reduction onto the non-zero momentum level, in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimle…

A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…

Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some…

We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…

The semiclassical approximation of the worldline path integral is a powerful tool to study nonperturbative electron-positron pair creation in spacetime-dependent background fields. Finding solutions of the classical equations of motion,…

It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the…

This paper addresses the problem of finding shortest paths homotopic to a given disjoint set of paths that wind amongst point obstacles in the plane. We present a faster algorithm than previously known.

Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the…

In this paper the path integral technique is applied to the quantum motion on the Hermitian hyperbolic space HH(2). The Schr\"odinger equation on this space separates in 12 coordinate systems which are closely related to the coordinate…

We give a superfield formulation of the path integral on an arbitrary curved phase space, with or without first class constraints. Canonical tranformations and BRST transformations enter in a unified manner. The superpartners of the…

Systems with constraints pose problems when they are quantized. Moreover, the Dirac procedure of quantization prior to reduction is preferred. The projection operator method of quantization, which can be most conveniently described by…

Feynman's path integral is herein generalized to the nonextensive canonical density matrix based on Tsallis entropy. This generalization is done in two ways by using unnormalized and normalized constraints. Firstly, we consider the path…