Related papers: On Dirac's Delta Calculus
We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter controlling the length of spinors is introduced. For one…
The article deals with a number of the existings variants of direct calculation of amplitudes of processes with polarized Dirac particles. It is shown, that all of them are special cases of one and the same mathematical scheme. The…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
We have shown that in some region where the Euler integral of the first kind diverges, the Euler formula defines a generalized function. The connected of this generalized function with the Dirac delta function is found.
Using numerical, theoretical and general methods, we construct evaluation formulas for the Jacobi $\theta$ functions. Some of our results are conjectures, but are verified numerically.
The work analyzes the theory of Dunkl operator as a moment differential operator. This last operator generalizes the first one whenever the sequence of moments satisfies appropriate classical properties, classically considered in the…
An efficient solution of the Dirac Hamiltonian flow equations has been proposed through a novel expandsion with the inverse of the Dirac effective mass. The efficiency and accuracy of this new expansion have been demonstrated by reducing a…
In the present paper it is shown that the Dirac electron theory is the approximation of the special nonlinear electromagnetic field theory
The paper is concerned with the completeness property of root functions of the $2\times 2$ Dirac operator with summable complex-valued potential and non-regular boundary conditions. Sufficient conditions for the completeness of the root…
A formal description of a functional analysis approach to the Riemann zeta-functional equation that provides in principle an infinity of different proofs based on work by the author on the existence of dilation-invariant unitary operators…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
A formulation of Dirac's equation using complex-quaternionic coordinates appears to yield an enormous gain in formal elegance, as there is no longer any need to invoke Dirac matrices. This formulation, however, entails several…
We give a half-page proof of the Lagrange-Good formula, using the Fourier representation of Dirac delta function.
We prove general necessary optimality conditions for delta-nabla isoperimetric problems of the calculus of variations.
A peculiar representation of the Lorentz group is suggested as a starting point for a consistent approach to relativistic quantum theory.
An elementary treatment of the Dirac Equation in the presence of a three-dimensional spherically symmetric $\delta (r-r_0)$-potential is presented. We show how to handle the matching conditions in the configuration space, and discuss the…
In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in our previous works, and a generalized Mortici's lemma.
The Dirac oscillators are shown to be an excellent expansion basis for solutions of the Dirac equation by $R$-matrix techniques. The combination of the Dirac oscillator and the $R$-matrix approach provides a convenient formalism for…
After the short survey of the Klein Paradox in 3-dimensional relativistic equations, we present a detailed consideration of Dirac modified equation, which follows by one particle infinite overweighting in Salpeter Equation. It is shown,…
We introduce the notion of "\delta-complete decision procedures" for solving SMT problems over the real numbers, with the aim of handling a wide range of nonlinear functions including transcendental functions and solutions of…