Two-spinors and Einstein- Cartan- Maxwell-Dirac fields*

Two-spinors and Einstein- Cartan-Maxwell-Dirac fields*

Daniel Canarutto

Dipartimento di Matematica Applicata "G. Sansone, Via S. Marta 3, 50139 Firenze, Italia

Arkadiusz Jadczyk

Institute of Theoretical Physics, pl. Maksa Borna 9, 50-204 Wroclaw, Poland

Abstract

We show that a complex vector bundle S to M, where M is a 4-dimensional real manifold and the fibres of S are 2-dimensional, yields in a natural way all structures which are needed in order to formulate a (classical) theory of Einstein-Cartan-Maxwell-Dirac fields. Namely, all needed bundles and their fibre structures follow from functorial constructions with no further assumptions. Any considered object which is not a functorial construction is taken to be a field. This is true even for coupling constants, which arise as constant sections of real line bundles derived form S. In the above said context we also discuss to what extend one can give a formulation which is not singular in the case of a degenerate vierbein

1991 MSC:

Keywords: two-spinors, connections, Einstein-Cartan fields, vierbein, Dirac fields, Maxwell fields, dilaton.

Contents:

1. Preliminaries

2. Two-spinor algebra

3. Two-spinor connections

4. Soldering form (vierbein)

5. Fileds and field equations

"This work has been supported by Italian MURST (national and local funds) and by GNFM of the Consiglio Nazionale delle Ricerche.

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