arXiv subjects

Francis Atta Howard

Publications and source records attributed to Francis Atta Howard.

5 recordsLinked to original sources

arXiv2026

Gertsch quotient living in the "poor man's adele ring" $\mathcal{A}$: Kurepa-Bell-Wilson congruence

Wilson's theorem is notably related to left factorials, expressed as $K_p \equiv \mathbf{Bell}_{p-1} - 1 \pmod p$, for prime $p\geq3$. This study examines a Kurepa-Bell-Wilson congruence (\textbf{KBW}), $\frac{K_p + 1}{p}\equiv \frac{ \mathbf{Bell}_{p-1}}{p}+ W_p \pmod{p}$, and demonstrates that it naturally generates the non-zero "Gertsch quotient ($\mathbb{G}_p$)," which, for larger primes modulo $p$ resides in the poor man's adele ring $\mathcal{A}$ .

math.GM↗

arXiv2025

Isomorphisms of $\Spin\left( \frac{1}{2}\right) $ to $\SU(1,1)-\mbox{Boson}$: Universal Enveloping and Kangni-type Transformation

In this study we investigate the nexus between the $\Spin (\frac12)$ and the $\SU(1,1)$-quasi boson Lie structure and reveal related properties as well as some decomposition of spin particles. We show that the $\SU(1,1)$-quasi boson has a left invariant Haar measure and we ascertain its spherical Fourier transformation. We finally show that this spherical Fourier transformation of type delta is a Kangni-type transform when the Planck's constant, $\hbar=1$.

math-ph↗

arXiv2025

Partition Functions and Kurepa Decomposition I: Algebraic computation and some physical Applications

This paper examines the algebraic features of notable polynomial functions and explores their combinatorial aspects by presenting precise decompositions in terms of Dobinski numbers, Bell numbers, and moments generating functions. Additionally, a new equivalence to the Kurepa factorial is developed to help investigate the Kurepa conjecture. In conclusion, we examine several physical phenomena related to Kurepa factorials, occupation number, Fermi-Dirac and Bose-Einstein distributions while exploring their algebraic characteristics.

math.CO↗

arXiv2023

Particles and $p-$adic integrals of Spin$\left(\frac{1}{2}\right)$: spin Lie group, $\mathcal{R}(ρ,q)-$gamma and $\mathcal{R}(ρ,q)-$ beta functions, ghost and applications

In this work, we address the $p$-adic analogues of the fermion spin Lie algebras and Lie groups. We consider the extension of the fermion spin Lie groups and Lie algebras to the $p-$adic Lie groups and investigate the way to extend their integral to the zeta function as well. We show that their groups are ghost friendly. In addition, we develop the $\mathcal{R}(p,q)-$deformed calculus for the Bernoulli, Volkenborn, Euler and Genocchi polynomials, and establish related definitions. Finally, we perform a $p-$adic generalization of beta and gamma functions and exhibit some physical applications.

math.NT↗

arXiv2020

Group-algebraic characterization of spin particles: semi-simplicty, SO(2N) structure and Iwasawa decomposition

In this paper, we focus on the characterization of Lie algebras of fermionic, bosonic and parastatistic operators of spin particles. We provide a method to construct a Lie group structure for the quantum spin particles. We show the semi-simplicity of a quantum spin particle Lie algebra, and extend the results to the Lie group level. Besides, we perform the Iwasawa decomposition of spin particles at both the Lie algebra and Lie group levels. Finally, we investigate the coupling of angular momenta of spin half particles, and give a general construction for such a study.

math-ph↗