Dotted and Undotted Algebraic Spinor Fields in General Relativity

Details Dotted and Undotted Algebraic Spinor Fields in General Relativity Dotted and Undotted Algebraic Spinor Fields in General Relativity

2004-07-13

arxiv.org/abs/math-ph/0407024v3

Int.J.Mod.Phys. D13 (2004) 1637-1660; Erratum-ibid. D14 (2005) 185

Physics

Mathematical Physics

some new misprints have been corrected

Scientific paper

10.1142/S0218271804005201

We investigate using Clifford algebra methods the theory of algebraic dotted and undotted spinor fields over a Lorentzian spacetime and their realizations as matrix spinor fields, which are the usual dotted and undotted two component spinor fields. We found that some ad hoc rules postulated for the covariant derivatives of Pauli sigma matrices and also for the Dirac gamma matrices in General Relativity cover important physical meaning, which is not apparent in the usual matrix presentation of the theory of two components dotted and undotted spinor fields. We also discuss some issues related to the the previous one and which appear in a proposed "unified" theory of gravitation and electromagnetism which use two components dotted and undotted spinor fields and also paravector fields, which are particular sections of the even subundle of the Clifford bundle of spacetime.

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