Related papers: Path integral in a magnetic field using the Trotte…
A generalized Feynman-Kac formula based on the Wiener measure is presented. Within the setting of a quantum particle in an electromagnetic field it yields the standard Feynman-Kac formula for the corresponding Schr\"odinger semigroup. In…
We give a new proof of the trace formula for regular graphs. Our approach is inspired by path integral approach in quantum mechanics, and calculations are mostly combinatorial.
Path-integral approach to the tight-binding polaron is extended to multiple optical phonon modes of arbitrary dispersion and polarization. The non-linear lattice effects are neglected. Only one electron band is considered. The…
Using mean-field theory, we compute the evolution of the magnetic field in a cylinder with outer perfectly conducting boundaries, an imposed axial magnetic and electric field. The thus injected magnetic helicity in the system can be…
A real-time path integral for ultrasoft QCD is formulated. It exhibits a Feynman's influence functional. The statistical properties of the theory and the gauge symmetry are explicit. The correspondence is established with the alternative…
Using the path integral measure factorization method based on the nonlinear filtering equation from the stochastic process theory, we consider the reduction procedure in Wiener path integrals for a mechanical system with symmetry that…
Path integrals developed by Richard Feynman have been an important tool in Physics in studying quantum field theory. In mathematics, it has also been widely used in providing formal proofs in the study of Index theorem and asymptotic…
Phase space path integral is worked out in a riemannian geometry, by employing a prescription for the infinitesimal propagator that takes riemannian normal coordinates and momenta on an equal footing. The operator ordering induced by this…
The path integral approach is used for the calculation of the correlation functions of the $XY$ Heisenberg chain. The obtained answers for the two-point correlators of the $XX$ magnet are of the determinantal form and are interpreted in…
A method based on the path integral approach is engaged to consider the gravitational emission from a quantum mechanical bound system in a locally inertial frame. In such a frame, interaction between the electromagnetic (bound potential)…
The Feynman path integral for nonrelativistic quantum electrodynamics is studied mathematically of a standard model in physics, where the electromagnetic potential is assumed to be periodic with respect to a large box and quantized thorough…
We calculate stationary probability distribution of magnetic field, generated by moving charges of plasma environment, and stationary probability distribution of force, acting on charged particle in this environment, with magnetic…
In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and…
A path-integral approach to lattice polarons is developed. The method is based on exact analytical elimination of phonons and subsequent Monte Carlo simulation of self-interacting fermions. The analytical basis of the method is presented…
The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to…
A new method ( PI-DFT ) which combines path integrals and density functional theory is proposed as a pathway to many fields of physics. Within path integral theory it is possible to construct particle densities without explicitly…
The ferrofluid dynamics theory is applied to thermodiffusive problems in magnetic fluids in the presence of magnetic fields. The analytical form for the magnetic part of the chemical potential and the most general expression of the mass…
The functional integration scheme for path integrals advanced by Cartier and DeWitt-Morette is extended to the case of fields. The extended scheme is then applied to quantum field theory. Several aspects of the construction are discussed.
We present a way for calculating the Lagrangian path integral measure directly from the Hamiltonian Schwinger--Dyson equations. The method agrees with the usual way of deriving the measure, however it may be applied to all theories, even…
An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…