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Type: Artigo de Periódico
Title: A Clifford Bundle Approach To The Wave Equation Of A Spin 1/2 Fermion In The De Sitter Manifold
Author: Rodrigues
WA; Wainer
SA; Rivera-Tapia
M; Notte-Cuello
EA; Kondrashuk
Abstract: In this paper we give a Clifford bundle motivated approach to the wave equation of a free spin 1/2 fermion in the de Sitter manifold, a brane with topology living in the bulk spacetime and equipped with a metric field with being the inclusion map. To obtain the analog of Dirac equation in Minkowski spacetime in the structure we appropriately factorize the two Casimir invariants C (1) and C (2) of the Lie algebra of the de Sitter group using the constraint given in the linearization of C (2) as input to linearize C (1). In this way we obtain an equation that we called DHESS1, which in previous studies by other authors was simply postulated. Next we derive a wave equation (called DHESS2) for a free spin 1/2 fermion in the de Sitter manifold using a heuristic argument which is an obvious generalization of a heuristic argument (described in detail in Appendix D) permitting a derivation of the Dirac equation in Minkowski spacetime and which shows that such famous equation express nothing more than the fact that the momentum of a free particle is a constant vector field over timelike integral curves of a given velocity field. It is a remarkable fact that DHESS1 and DHESS2 coincide. One of the main ingredients in our paper is the use of the concept of Dirac-Hestenes spinor fields. Appendices B and C recall this concept and its relation with covariant Dirac spinor fields usually used by physicists.
Subject: De Sitter Manifold
Clifford Bundle
Dirac Equation
Citation: Advances In Applied Clifford Algebras. SPRINGER BASEL AG, n. 26, n. 1, p. 253 - 277.
Rights: fechado
Identifier DOI: 10.1007/s00006-015-0588-z
Date Issue: 2016
Appears in Collections:Unicamp - Artigos e Outros Documentos

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