Related papers: The propagator for the step potential using the pa…
We present a derivation of the propagator for a particle in the presence of the step and delta function potentials. These propagators are known, but we present a direct path integral derivation, based on the path decomposition expansion and…
The path decomposition expansion is a path integral technique for decomposing sums over paths in configuration space into sums over paths in different spatial regions. It leads to a decomposition of the configuration space propagator across…
The path integral for the propagator is expanded into a perturbation series, which can be exactly summed in the case of $\delta$-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the…
The path decomposition expansion represents the propagator of the irreversible reaction as a convolution of the first-passage, last-passage and rebinding time probability densities. Using path integral technique, we give an elementary, yet…
Although driven Brownian particles are ubiquitous in stochastic dynamics and often serve as paradigmatic model systems for many aspects of stochastic thermodynamics, fully analytically solvable models are few and far between. In this paper,…
In this and subsequent paper arXiv:1011.5185 we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible…
We show how the induction law is correctly used in the path integral computation of the free particle propagator. The way this primary path integral example is treated in most textbooks is a little bit missleading.
A number of approaches to the arrival time problem employ a complex potential of a simple step function type and the arrival time distribution may then be calculated using the stationary scattering wave functions. Here, it is shown that in…
The motion of a particle in the field of dispiration (due to a wedge disclination and a screw dislocation) is studied by path integration. By gauging $SO(2) \otimes T(1)$, first, we derive the metric, curvature, and torsion of the medium of…
The propagator associated to the potential barrier $V=V_{0}\cosh ^{-2}(\omega x)$ is obtained by solving path integrals. The method of delta functionals based on canonical and other transformations is used to reduce the path integral for…
We consider a simple action for a fractional spin particle and a path integral representation for the propagator is obtained in a gauge such that the constraint embodied in the Lagrangian is not an obstacle. We obtain a propagator for the…
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the…
It is of interest in a variety of contexts, and in particular in the arrival time problem, to consider the quantum state obtained through unitary evolution of an initial state regularly interspersed with periodic projections onto the…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
We study approximations of Feynman path integrals in finite dimensional spaces and how the approximations determine the propagator.
A specific class of explicitly time-dependent potentials is studied by means of path integrals. For this purpose a general formalism to treat explicitly time-dependent space-time transformations in path integrals is sketched. An explicit…
We address a number of aspects of the arrival time problem defined using a complex potential of step function form. We concentrate on the limit of a weak potential, in which the resulting arrival time distribution function is closely…
Discontinuous initial wave functions or wave functions with discontintuous derivative and with bounded support arise in a natural way in various situations in physics, in particular in measurement theory. The propagation of such initial…
Given any (Feynman) propagator which is Lorentz and translation invariant, it is possible to construct an action functional for a scalar field such that the quantum field theory, obtained by path integral quantization, leads to this…
We examine the problem of the evaluation of both the propagator and of the partition function of a spinning particle in an external field at the classical as well as the quantum level, in connection with the asserted exactness of the saddle…