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

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