Related papers: Nonlocal Dirac Equation for Accelerated Observers
We discuss the generalization of the Dirac equations and spinors in momentum space to free unstable spin-$1/2$ fermions taking into account the fundamental requirement of Lorentz covariance. We derive the generalized adjoint Dirac equations…
It was previously shown that models with deformations of special relativity that have an energy-dependent yet observer-independent speed of light suffer from nonlocal effects that are in conflict with observation to very high precision. In…
We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincar\'e invariance. We determine the constraints…
A shifted or misaligned feedback loop gives rise to a two-point nonlocality that is the spatial analog of a temporal delay. Important consequences of this nonlocal coupling have been found both in diffusive and in diffractive systems, and…
A general method for extending a non-dissipative nonlinear Schr\"odinger and Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles is described. It is shown at a general level that the dynamics so obtained is…
We obtain the local well-posedness for Dirac equations with a Hartree type nonlinearity derived by decoupling the Dirac-Klein-Gordon system. We extend the function space of initial data, enabling us to handle initial data that were not…
The Dirac equation is invariant under rotations with a constant frequency and invariable cylindrical radius. 3D transformation for rotating frames is found with help of this invariance. Exact localized solutions of the Dirac equation in the…
We explore nonlocally modified models of gravity, inspired by quantum loop corrections, as a mechanism for explaining current cosmic acceleration. These theories enjoy two major advantages: they allow a delayed response to cosmic events,…
The nonlocal electrodynamics of uniformly rotating systems is presented and its predictions are discussed. In this case, due to paucity of experimental data, the nonlocal theory cannot be directly confronted with observation at present. The…
We address the problem of detecting non-locality in coupled N level systems in the language of spin. Through a number of examples, we show that non-locality can be detected via a violation of the standard Bell inequality, irrespective of…
We study the retarded field sourced by a uniformly accelerated particle in a non-local scalar field theory. While the presence of non-locality regularizes the field at the location of the source, we also show that Lorentz-invariant…
A set of pointwise estimates are established for local solutions to nonlocal diffusion equations with a drift term. In particular, our Harnack estimates are the first ones for such equations, and our H\"older regularity refines certain…
We consider two spacelike separated Dirac particles and construct five invariants under the spinor representations of the local proper orthochronous Lorentz groups. All of the constructed Lorentz invariants are identically zero for product…
We revisit acceleration-induced nonlocal electrodynamics and the phenomenon of photon spin-rotation coupling. The kernel of the theory for the electromagnetic field tensor involves parity violation under the assumption of linearity of the…
Nonlocal electrodynamics is a formalism developed to include nonlocal effects in the measurement process caused by the non-inertial state of the observers. This theory modifies Maxwell's electrodynamics by eliminating the hypothesis of…
Using condition of relativistic invariance, group theory and Clifford algebra the component Lorentz invariance generalized Dirac equation for a particle with arbitrary mass and spin is suggested, where In the case of half-integral spin…
We study the role of acceleration in the twin paradox. From the coordinate transformation that relates an accelerated and an inertial observer we find that, from the point of view of the accelerated observer, the rate of the differential…
We propose a novel nonlocal spin-1/2 theory in which the form factor depends on the Dirac operator rather than on the d'Alembert operator. In this scenario, we explore some classical and quantum aspects of this new theory. At the classical…
A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstantaneous scattering integral in the spirit of Enskog corrections is discussed. Numerical values of the…
The aim of this article is to develop the regularity theory for parabolic equations driven by nonlocal operators associated with nonsymmetric forms. H\"older regularity and weak Harnack inequalities are proved using extensions of recently…