Related papers: On Dirac's Delta Calculus
It is shown that the squared operation of the Dirac equation which is widely applied may create new solutions and moreover may change the inner nature of original equation. Some illustrating examples are considered as well.
The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of Morera theorem, because distributional Cauchy-Riemann…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with…
While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants…
The nilpotent Dirac formalism has been shown, in previous publications, to generate new physical explanations for aspects of particle physics, with the additional possibility of calculating some of the parameters involved in the Standard…
A closed formula multiallelic Walsh (or Hadamard) transform is introduced. Basic results are derived, and a statistical interpretation of some of the resulting linear forms is discussed.
The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger like one. Earlier results are…
The Dirac's bra-ket formalism is generalized to finite-dimensional vector spaces with indefinite metric in a simple mathematical context similar to thatof the theory of general tensors where, in addition, scalar products are introduced with…
Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac…
On the basis of analysis on the adele ring of any algebraic numbers field (Tate's formula) a regularization for divergent adelic products of gamma- and beta-functions for all completions of this field are proposed, and corresponding…
We develop a complete Dirac's canonical analysis for an alternative action that yields Maxwell's four-dimensional equations of motion. We study in detail the full symmetries of the action by following all steps of Dirac's method in order to…
If $T$ is a (densely defined) self-adjoint operator acting on a complex Hilbert space $\mathcal{H}$ and $I$ stands for the identity operator, we introduce the delta function operator $\lambda \mapsto \delta \left(\lambda I-T\right) $ at…
We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.
The Dirac equation is considered in the background of potentials of several types, namely scalar and vector-potentials as well as "Dirac-oscillator" potential or some of its generalisations. We investigate the radial Dirac equation within a…
We postulate a new nonlinear generalization of the Dirac equation for an electron. Basic properties of the new equation are considered.
Whereas the Dirac delta function introduced by P. A. M. Dirac in 1930 in his famous quantum mechanics text has been well studied, a not famous formula related to the delta function using the Heaviside step function in a single-variable…
The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail…
The purpose of this paper is to generalize the regular Optimal Reduction Theorem to general proper Dirac actions, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given…
So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well…