, Volume 16, Issue 8, pp 701-719

Relativistic algebraic spinors and quantum motions in phase space

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Abstract

Following suggestions of Schönberg and Bohm, we study the tensorial phase space representation of the Dirac and Feynman-Gell-Mann equations in terms of the complex Dirac algebra C4, a Jordan-Wigner algebra G4, and Wigner transformations. To do this we solve the problem of the conditions under which elements in C4 generate minimal ideals, and extend this to G4. This yields the linear theory of Dirac spin spaces and tensor representations of Dirac spinors, and the spin-1/2 wave equations are represented through fermionic state vectors in a higher space as a set of interconnected tensor relations.