Combined Theory of Basis Sets of Spinors for Particles with Arbitrary Spin in Position, Momentum and Four-Dimensional Spaces

TL;DR

This paper develops a comprehensive theory for basis spinors of particles with any spin in various spaces, facilitating solutions to generalized Dirac equations using specialized relativistic spinor basis functions.

Contribution

It introduces a unified framework for relativistic basis spinors of arbitrary spin particles across multiple spaces, reducing them to simpler components for computational applications.

Findings

Established basis spinors for arbitrary spin particles in multiple spaces.

Reduced complex spinors to simpler one- and two-component forms.

Provided relations useful for atomic orbital approximations in relativistic quantum mechanics.

Abstract

The 2(2s+1)-component relativistic basis spinors for the arbitrary spin particles are established in position, momentum and four-dimensional spaces, where s=0,1 / 2,1, 3 / 2, 2, ... . These spinors for integral- and half-integral spins are reduced to the independent sets of one- and twocomponent spinors, respectively. Relations presented in this study can be useful in the linear combination of atomic orbitals approximation for the solution of generalized Dirac equation of arbitrary spin particles introduced by the author when the orthogonal basis sets of relativistic exponential type spinor wave functions and Slater type spinor orbitals in position, momentum and four -dimensional spaces are employed.