Related papers: Calculating propagators for relativistic wave equa…
Superstatistics permits the calculation of the Feynman propagator of a relativistic particle in a novel way from a superstatistical average over non-relativistic single-particle paths. We illustrate this for the Klein-Gordon particle in the…
We develop a theory of Feynman propagators for the massive Klein--Gordon equation with asymptotically static perturbations. Building on our previous work on the causal propagators, we employ a framework based on propagation of singularities…
By appeal to Distribution Theory we discuss in rigorous fashion, without appealing to {\bf any conjecture} (as usually done by other authors), the boundary-bulk propagators for the scalar field, both in the non-massive and massive cases.…
The relativistic wave equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave, in a medium of index of refraction n_m < 1, have been studied. In the Dirac case the found exact solutions…
Representations of the Klein-Gordon and Dirac propagators are determined in a $N$ dimensional conical background for massive fields twisted by an arbitrary angle $2\pi\sigma$. The Dirac propagator is shown to be obtained from the…
We prove global in time dispersion for the wave and the Klein-Gordon equation inside the Friedlander domain by taking full advantage of the space-time localization of caustics and a precise estimate of the number of waves that may cross at…
The propagator of the discrete Schr\"odinger equation is computed and its properties are revealed through a Feynman path summation in discrete space. Initial data problems such as diffraction in discrete space and continuous time are…
In this article, we analyze the fundamental global and local symmetries involved in the action for the free relativistic point particle. Moreover, we identify a hidden local symmetry, whose explicit consideration and factorization utilizing…
A quantum mechanical description of particle propagation on the discrete spacetime of a causal set is presented. The model involves a discrete path integral in which trajectories within the causal set are summed over to obtain a particle…
We consider a relativistic charged particle in a background scalar field depending on both space and time. Poincar\'e, dilation and special conformal symmetries of the field generate conserved quantities in the charge motion, and we exploit…
The Cauchy problem for the massive Dirac equation is studied in the Reissner-Nordstr\"om geometry in horizon-penetrating Eddington-Finkelstein-type coordinates. We derive an integral representation for the Dirac propagator involving the…
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…
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…
The 3+1 spacetime formulation of general relativity is used to investigate the transverse waves propagating in a plasma influenced by the gravitational field of Reissner-Nordstrom black hole, as explained in an earlier paper, to take…
Recently, solutions of the Ishibashi, Kawai, Kitazawa and Tsuchiya matrix theory have been found, which can be interpreted as 3+1-dimensional quantum geometries describing an effective Friedmann-Lema\^{i}tre-Robertson-Walker cosmology with…
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…
We discuss two distinct operator-theoretic settings useful for describing (or defining) propagators associated with a scalar Klein-Gordon field on a Lorentzian manifold $M$. Typically, we assume that $M$ is globally hyperbolic. The term…
We use a light-cone approach to solve the Schwinger-Dyson equation for the quark propagator. We show how this method can be used to solve the equation beyond the space-like region, to which one is usually restricted with the usual…
We analyze the propagation of two-dimensional dispersive and relativistic wavepackets localized in the vicinity of the zero level set $\Gamma$ of a domain wall. The main applications we consider are a topologically non-trivial Dirac model…
We consider second order differential operators with coefficients which are Gaussian random fields. When the covariance becomes singular at short distances then the propagators of the Schr\"odinger equation as well as of the wave equation…