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

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.