arXiv subjects

Kikunga Kasenda Ivan

Publications and source records attributed to Kikunga Kasenda Ivan.

3 recordsLinked to original sources

arXiv2025

Factorization, Supersymmetry, Coherent States and Classical Trajectories

A generalization of coherent states has been developed in the context of supersymmetric quantum mechanics. For many cases, no link has been made with the corresponding classical system. In this work, we consider simple superpotentials and compare the classical trajectories and the mean values of the position operator in these states. The mean value of the position operator can be written as a power series in time with coefficients whose relations to the superpotential are given in the general case. These coefficients imply integrals and recursion formulas. The method used reproduces exactly what is known for the harmonic oscillator. It is extended to study a family of systems which encompasses the harmonic oscillator. We also consider a third degree superpotential. The time scale after which the mean value of the position operator and the classical trajectory begin differing significantly is evaluated. Keywords: Coherent States, SUSYQM.

hep-th↗

arXiv2023

The Higgs Boson and The Fakeon Hypothesis

In this paper, we make an attempt to implement the fakeon hypothesis in particle physics. To begin with, we consider a model in which the Higgs boson is the only fakeon. We deduce its interactions with the electroweak gauge bosons. Each such new interaction can be written as a product of two factors. The first one depends, on the electroweak gauge bosons and their derivatives. The second one solely depends, on the physical Higgs and its derivatives. We also study the conserved quantities of different (free) fields in this setting.

hep-ph↗

arXiv2019

On a Family of Hypergeometric Polynomials

We work on the SCE problems. We establish the expressions of three integrals' sequences, related to it, in terms of five families of polynomials. Relations between these integrals are demonstrated and we focus on one of the three problems : the determination of the family of polynomials noted $e_n (n \in \mathbb{N})$. We show taht these polynomials are hypergeometric. From this property, the NU method can be applied to this family. We have been able to determine the Rodrigues formula. These polynomials have properties that distinguish them from classical hypergeometric polynomials. We state and demonstrate the theorem adapted to the determination of the generating function of $e_n$. Finally, the sequence of polynomials studied is expressed in terms of associated Laguerre polynomials with negative upper indices.

math.CA↗