Related papers: Angular Functions with Complex Angular Momenta
A useful finite-dimensional matrix representation of the derivative of periodic functions is obtained by using some elementary facts of trigonometric interpolation. This NxN matrix becomes a projection of the angular derivative into…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
It is shown that solutions to the 2nd order BFKL eigenvalue equation exist for arbitrary large real values of the complex angular momentum $j$. This corresponds to a cut in the complex $j$ plane along the whole real axis, and it makes the…
A consistent analytical approach for calculation of the quasiclassical radial dipole matrix elements in the momentum and coordinate representations is presented. Very simple but relatively precise expressions for the matrix elements are…
Often it is asserted that only by using of the symmetric Landau-Lifschitz energy-momentum complex one is able to formulate a conserved angular momentum complex in General Relativity ({\bf GR}). Obviously, it is an uncorrect statement. For…
Processes with oppositely charged spinor particles in initial and/or final states in homogeneous magnetic field B are subject to focusing effects in their relative motion, which yield the amplifying factors in probabilities growing as $eB$.…
We derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse L\'evy-subordinator. If the time change is inverse $\alpha$-stable, the time-derivative…
We study integral expressions of electromagnetic multipole moments of arbitrary order in Cartesian coordinates. The volume and surface integrals of charge-induced and current-induced multipole moment tensors are formulated and the…
Exact stationary solutions of the wave equation are obtained to describe the interaction between magnetic moment of elementary particle and circularly polarized photons. The obtained solutions substantially modify the conventional model of…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
The simplest nontrivial tau functions of the Toda lattice and the $\tN$-component Toda lattice are compared in their applications to multimatrix integrals.
Covariantly we reformulate the description of a spinning particle in terms of the Poincar\'{e} group. We also construct a Lagrangian which entails all possible constraints explicitly; all constraints can be obtained just from the…
We introduce matching functions as a means of summing heavy-quark logarithms to any order. Our analysis is based on Witten's approach, where heavy quarks are decoupled one at a time in a mass-independent renormalization scheme. The outcome…
This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…
The technique of functional integration over velocities is applied to the calculation of the propagator of a spinning particle with and without anomalous magnetic moment. A representation for the spin factor is obtained in this context for…
We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-Konig and Zeller type operators are elementary functions. The higher order moments of these operators…
A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.
In this paper we introduce and study three classes of fractional periodic processes. An application to ring polymers is investigated. We obtain a closed analytic expressions for the form factors, the Debye functions and their asymptotic…
In this paper, we extend to polarization the method we have recently employed to treat spin. We are led to a generalization of its treatment. Thus, we are able to connect its matrix treatment to first principles, and we obtain the most…