Related papers: Schwinger's Propagator Is Only A Green's Function
Efficient computation methods are devised for the perturbative solution of Schwinger--Dyson equations for propagators. We show how a simple computation allows to obtain the dominant contribution in the sum of many parts of previous…
We present a novel, highly efficient yet accurate analytical approximation for the Green's function of a Holstein polaron. It is obtained by summing all the self-energy diagrams, but with each self-energy diagram averaged over the momenta…
The 2D space-fractional Schrodinger equation in the time-independent and time-dependent cases for the scattering problem in the fractional quantum mechanics is studied. We define and give the mathematical expression of the Green's functions…
We study the role of the Schwinger phase (SP) that appears in the propagator of a charged particle in the presence of a static and uniform magnetic field $\vec{B}$. We first note that this phase cannot be removed by a gauge transformation;…
We prove a unique continuation principle or uncertainty relation valid for Schr\"odinger operator eigenfunctions, or more generally solutions of a Schr\"odinger inequality, on cubes of side $L\in 2\NN+1$. It establishes an equi-distribution…
Employing methods introduced by Schwinger in quantum electrodynamics, we compute the propagator for a non-Abelian gauge field in a plane wave background field. In the long distance limit a mass-like term for the gauge field is induced by…
A method for the computation of scattering data and of the Green function for the one-dimensional Schr\"{o}dinger operator $H:=-\frac{d^2}{dx^2}+q(x)$ with a decaying potential is presented. It is based on representations for the Jost…
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 study the probability distribution of the number of particle and antiparticle pairs produced via the Schwinger effect when a uniform but time-dependent electric field is applied to noninteracting scalars or spinors initially at a…
We numerically investigate the temporal behavior and the structure of longitudinal momentum spectrum and the field polarity effect on pair production in pulsed electric fields in scalar quantum electrodynamics (QED). Using the evolution…
In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are…
The evolution equation for the propagator of the quantum system in the optical probability representation (optical propagator) is obtained. The relations between the optical and quantum propagators for the Schr\"odinger equation and the…
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…
It has been shown that the Schwinger-Dyson equations for non-Hermitian theories implicitly include the Hilbert-space metric. Approximate Green functions for such theories may thus be obtained, without having to evaluate the metric…
In this work, a constant and uniform magnetic field is less than the Schwinger critical value. In turn, an additional constant and uniform electric field is taken much smaller than the magnetic field value. The propagation of a photon in…
In this paper, we study time decay estimates for the Schr\"odinger propagator on the product cone $(X,g)$, where $X=C(\rho \mathbb{S}^{n-1})=(0,\infty)\times \rho\mathbb{S}^{n-1}$. We prove that the usual dispersive estimate holds when the…
We analytically investigate the Schwinger pair production in the de Sitter background by using {\em the uniform asymptotic approximation method}, and show that the equation of motion in general has two turning points, and the nature of…
We show explicitly that Schwinger's formula for one-loop effective actions corresponds to the summation of energies associated with the zero-point oscillations of the fields. We begin with a formal proof, and after that we confirm it using…
Using a generalized transfer matrix method we exactly solve the Schr\"odinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating…
We review recent and give some new results on the spectral properties of Schroedinger operators with a random potential of alloy type. Our point of interest is the so called Wegner estimate in the case where the single site potentials…