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

TL;DR

This paper explores $p$-adic analogues of fermion spin Lie groups and algebras, extending their integrals to zeta functions, developing deformed calculus, and generalizing beta and gamma functions with physical applications.

Contribution

It introduces the extension of fermion spin Lie groups to $p$-adic settings, develops $ ho,q$-deformed calculus, and generalizes classical functions with applications in physics.

Findings

Groups are ghost friendly.

Developed $ ho,q$-deformed calculus for special polynomials.

Established $p$-adic generalizations of beta and gamma functions.

Abstract

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.