Related papers: Calculating propagators for relativistic wave equa…
For the special case of freely evolving Dirac electrons in $1 + 1$ dimensions, Feynman checkerboard paths have previously been used to derive Wigner's arrival-time distribution which includes all arrivals. Here, an attempt is made to use…
The third part of the paper is devoted to ray tracing in optical resonators. The employed method for dealing with the issue uses the elliptical or hyperbolic rotations that Wigner distributions associated with optical fields undergo during…
Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic…
The Schwinger-Dyson equation for a scalar propagator is solved in Minkowski space with the help of an integral spectral representation, both for spacelike and timelike momenta. The equation is re-written into a form suitable for numerical…
We consider the propagation of a generic scalar field around a rotating and charged black hole. Using the partial wave method, we find, numerically, the total and partial absorption cross sections for different incidence angles. We…
A major challenge of many diffraction calculations, using some form of the Rayleigh-Sommerfeld formulas, is the integration of a highly oscillatory integrand. Here we derive a potentially useful alternative form of solution to the Helmholtz…
We construct the causal (forward/backward) propagators for the massive Klein-Gordon equation perturbed by a first order operator which decays in space but not necessarily in time. In particular, we obtain global estimates for…
The paper analyzes time propagation of Dirac observables - using Heisenberg representation - in the light of various pseudodifferential operator algebras (cf. [Co3], [Co15], [Co16]). Our theory gives (i) a mechanical angular momentum (the…
In this work we study the Dirac equation on the cosmic string background, which models a one--dimensional topological defect in the spacetime. We first define the Dirac operator in this setting, classifying all of its selfadjoint…
The symmetries of a scalar field theory in multifractional spacetimes are analyzed. The free theory realizes the Poincar\'e algebra, and the associated symmetries are modifications of ordinary translations and Lorentz transformations. In…
We solve the Klein-Gordon equation in the presence of the hyperbolic tangent potential. The scattering solutions are derived in terms of hypergeometric functions. The reflection $R$ and transmission $T$ coefficients are calculated in terms…
The Dirac equation in $\mathbb{R}^{1,3}$ with potential Z/r is a relativistic field equation modeling the hydrogen atom. We analyze the singularity structure of the propagator for this equation, showing that the singularities of the…
We give an alternative proof of the completeness of the Chandrasekhar ansatz for the Dirac equation in the Kerr-Newman metric. Based on this, we derive an integral representation for smooth compactly supported functions which in turn we use…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…
This paper is devoted to the computation of discrete propagators in two-dimensional crystals and their application to a number of time dependent problems. The methods to compute such kernels are provided by a tight-binding representation of…
We simplify and generalize an approach proposed by Di Vecchia and Ravndal to describe a massive Dirac particle in external vector and scalar fields. Two different path integral representations for the propagator are derived systematically…
The phase shift due to the Sagnac Effect, for relativistic matter and electromagnetic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of…
We study free scalar field theory on flat spacetime using a background independent (polymer) quantization procedure. Specifically we compute the propagator using a method that takes the energy spectrum and position matrix elements of the…
In this paper we analyze the Feynman wave equation on Lorentzian scattering spaces. We prove that the Feynman propagator exists as a map between certain Banach spaces defined by decay and microlocal Sobolev regularity properties. We go on…