Related papers: Feynman integrals for non-smooth and rapidly growi…
The Feynman-Schwinger representation provides a convenient framework for the cal culation of nonperturbative propagators. In this paper we first investigate an analytically solvable case, namely the scalar QED in 0+1 dimension. With this…
A new type of integral representation is proposed for the propagators of the massive Klein-Gordon field minimally coupled to the gravity of the de Sitter expanding universe. This representation encapsulates the effects of the Heaviside step…
We study the convergence in $L^2$ of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the custom in Physics and Chemistry, the approximate propagators considered here…
We construct the Green functions (or Feynman's propagators) for the Schroedinger equations of the form $i\psi_{t}+{1/4}\psi_{xx}\pm tx^{2}\psi =0$ in terms of Airy functions and solve the Cauchy initial value problem in the coordinate and…
We study approximations of Feynman path integrals in finite dimensional spaces and how the approximations determine the propagator.
We outline a new approach to calculating the quantum mechanical propagator in the presence of geometrically non-trivial Dirichlet boundary conditions based upon a generalisation of an integral transform of the propagator studied in previous…
We consider functional Schr\"{o}dinger equations associated with a wide class of Hamiltonians in all Fock representations of the bosonic canonical commutation relations, in particular the Cook-Fock, Friedrichs-Fock, and Bargmann-Fock…
Perturbation series for the electron propagator in the Schwinger Model is summed up in a direct way by adding contributions coming from individual Feynman diagrams. The calculation shows the complete agreement between nonperturbative and…
We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schr\"odinger equation with a spatially and temporally random potential. Green's functions for the…
This paper considers the Schroedinger propagator on a cone with the conical singularity carrying magnetic flux (``flux cone''). Starting from the operator formalism and then combining techniques of path integration in polar coordinates and…
A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of…
Starting from Feynman's Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical…
We propose a Fresnel stochastic white noise framework to analyze the nature of the Feynman paths entering on the Feynman path integral expression for the Feynman propagator of aparticle quantum mechanically moving under an external…
We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman propagator of a particle quantum mechanically moving under a time…
We consider a class of linear Schroedinger equations in R^d, with analytic symbols. We prove a global-in-time integral representation for the corresponding propagator as a generalized Gabor multiplier with a window analytic and decaying…
On a large class of asymptotically flat spacetimes which includes radiative perturbations of Minkowski space, we define a distinguished global Feynman propagator for massive Klein-Gordon fields by means of the microlocal approach to…
We show in this paper how to construct Symanzik polynomials and the Schwinger parametric representation of Feynman amplitudes for gauge theories in an unspecified covariant gauge. The complete Mellin representation of such amplitudes is…
Let $V_\Gamma$ be a lattice periodic potential and $A$ and $\phi$ external electromagnetic potentials which vary slowly on the scale set by the lattice spacing. It is shown that the Wigner function of a solution of the Schroedinger equation…
The John-Nirenberg theorem states that functions of bounded mean oscillation are exponentially integrable. In this article we give two extensions of this theorem. The first one relates the dyadic maximal function to the sharp maximal…
In this paper, we correct an inaccurate result of previous works on the Feynman propagator in position space of a free Dirac field in (3+1)-dimensional spacetime, and we derive the generalized analytic formulas of both the scalar Feynman…