Related papers: Path integral on a manifold with a non-free group …

Certain natural geometric approximation schemes are developed for Wiener measure on a compact Riemannian manifold. These approximations closely mimic the informal path integral formulas used in the physics literature for representing the…

A path integral representation is given for the solutions of the 3+1 dimensional Dirac equation. The regularity of the trajectories, the non-relativistic limit and the semiclassical approximation are briefly mentioned.

Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…

I propose a path integral description of the Su-Schrieffer-Heeger Hamiltonian, both in one and two dimensions, after mapping the real space model onto the time scale. While the lattice degrees of freedom are classical functions of time and…

Path integrals and the Wilsonian renormalization group provide two complementary computational tools for investigating continuum approaches to quantum gravity. The starting points of these constructions utilize a bare action and a fixed…

We demonstrate that parastatistics can be quantized using path integrals by calculating the generating functionals for time-ordered products of both free and interacting parabose and parafermi fields in terms of path integrals. We also give…

In this paper, we prove a finite dimensional approximation scheme for the Wiener measure on closed Riemannian manifolds, establishing a generalization for $L^{1}$-functionals, of the approach followed by Andersson and Driver on [1]. We…

We present a path integral representation for massless spin one-half particles. It is shown that this gives us a super-symmetric, P-and T-non-invariant pseudoclassical model for relativistic massless spinning particles. Dirac quantization…

Path integral formulation based on the canonical method is discussed. Path integral for Yang-Mills theory is obtained by this procedure. It is shown that gauge fixing which is essential procedure to quantize singular systems by Faddeev's…

In this paper, we study partial automorphisms and, more generally, injective partial endomorphisms of a finite undirected path from Semigroup Theory perspective. Our main objective is to give formulas for the ranks of the monoids…

The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on…

The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…

In the path integral formulation of the partition function of quantum spin models, most current treatments employ the so-called static approximation to simplify the process of summing over all possible paths. Although sufficient for…

An isometric action of a Lie group on a Riemannian manifold is of cohomogeneity one if the corresponding orbit space is one-dimensional. In this article we develop a conceptual approach to the classification of cohomogeneity one actions on…

L\'{e}vy flights can be described using a Fokker-Planck equation which involves a fractional derivative operator in the position co-ordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show…

We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is…

The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…

We revisit the path integral description of the motion of a relativistic electron. Applying a minor but well motivated conceptional change to Feynman's chessboard model, we obtain exact solutions of the Dirac equation. The calculation is…

Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and…

The path integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and…