Related papers: Special comparison theorem for the Dirac equation
The non-perturbative solution to the strong CP problem with magnetic monopoles as originally proposed by the author is described. It is shown that the gauge orbit space with gauge potentials and gauge tranformations restricted on the space…
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…
It is argued from geometrical, group-theoretical and physical points of view that in the framework of QCD it is not only necessary but also possible to modify the Dirac equation so that correspondence principle holds valid. The Dirac wave…
We consider a linear impulsive system in an infinite-dimensional Banach space. It is assumed that the moments of impulsive action satisfy the averaged dwell-time condition and the linear operator on the right side of the differential…
A classical theorem of Landau states that, if an ordinary Dirichlet series has non-negative coefficients, then it has a singularity on the real line at its abscissae of absolute convergence. In this article, we relax the condition on the…
This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of…
We say that a finite subset $E$ of the Euclidean plane $\mathbb{R}^2$ has the discrete Pompeiu property with respect to isometries (similarities), if, whenever $f:\mathbb{R}^2\to \mathbb{C}$ is such that the sum of the values of $f$ on any…
Quantum mechanics in the presence of $\delta$-function potentials is known to be plagued by UV divergencies which result from the singular nature of the potentials in question. The standard method for dealing with these divergencies is by…
All Darboux integrable difference equations on the quad-graph are described in the case of the equations that possess autonomous first-order integrals in one of the characteristics. A generalization of the discrete Liouville equation is…
We study the concept of idempotence for relative monads, which exhibits several subtleties not present for non-relative monads. In particular, there is a bifurcation of notions of idempotence in the relative setting, which are…
A discrepancy principle for solving nonlinear equations with monotone operators given noisy data is formulated. The existence and uniqueness of the corresponding regularization parameter $a(\delta)$ is proved. Convergence of the solution…
We derive a boundary monotonicity formula for a class of biharmonic maps with Dirichlet boundary conditions. A monotonicity formula is crucial in the theory of partial regularity in super-critical dimensions. As a consequence of such a…
The v^2/c^2 expansion of the Dirac equation with external potentials is reexamined. A complete, gauge invariant form of the expansion to order (1/c)^2 is established which contains two additional terms, as compared to various versions…
A self consistent solution to Dirac equation in a Kerr Newman space-time with $M^2 > a^2 + Q^2$ is presented for the case when the Dirac particle is the source of the curvature and the electromagnetic field. The solution is localised,…
The Dirac equation is not semisimple. We therefore regard it as a contraction of a simpler decontracted theory. The decontracted theory is necessarily purely algebraic and non-local. In one simple model the algebra is a Clifford algebra…
We investigate in detail the problem of constructing magnetic monopole solutions within the finite-range electrodynamics (i.e., electrodynamics with non-zero photon mass, which is the simplest extension of the standard theory; it is fully…
We have studied the different symmetric properties of the generalized Maxwell's - Dirac equation along with their quantum properties. Applying the parity (\mathcal{P}), time reversal (\mathcal{T}), charge conjugation (\mathcal{C}) and their…
The relational formalism based on geometrical clocks and Dirac observables in linearized canonical cosmological perturbation theory is used to introduce an efficient method to find evolution equations for gauge invariant variables. Our…
We discuss a class of exact solutions of a three-parameter non-minimally extended Einstein-Maxwell model, which are attributed to non-minimal magnetic monopoles of the Dirac type. We focus on the investigation of the gravitational field of…
In this announcement we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We have shown that the…