Complexifying the spacetime algebra by means of an extra timelike dimension: Pin, Spin and algebraic spinors
Marcos R. A. Arcodía
Abstract:Because of the isomorphism Cl1,3(C) ≅ Cl2,3(R), it is possible to complexify the spacetime Clifford algebra Cl1,3(R) by adding one additional timelike dimension to the Minkowski spacetime. In a recent work we showed how this treatment provide a particular interpretation of Dirac particles and antiparticles in terms of the new temporal dimension. In this article we thoroughly study the structure of the real Clifford algebra Cl2,3(R) paying special attention to the isomorphism Cl1,3(C) ≅ Cl2,3(R) and the embeddi… Show more
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