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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Bilinear covariants and spinor fields duality in quantum Clifford algebras

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Autor(es):
Ablamowicz, Rafal [1] ; Goncalves, Icaro [2, 3] ; da Rocha, Roldao [3, 4]
Número total de Autores: 3
Afiliação do(s) autor(es):
[1] Tennessee Technol Univ, Dept Math, Cookeville, TN 38505 - USA
[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil
[3] Univ Fed ABC, Ctr Matemat Computacao & Cogn, BR-09210170 Santo Andre, SP - Brazil
[4] Int Sch Adv Studies SISSA, I-34136 Trieste - Italy
Número total de Afiliações: 4
Tipo de documento: Artigo Científico
Fonte: Journal of Mathematical Physics; v. 55, n. 10 OCT 2014.
Citações Web of Science: 23
Resumo

Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity {[}S. W. Hawking, ``The unpredictability of quantum gravity,{''} Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived. (C) 2014 AIP Publishing LLC. (AU)

Processo FAPESP: 12/07710-0 - Grupos clássicos em Álgebras de Clifford quânticas
Beneficiário:Ícaro Gonçalves
Linha de fomento: Bolsas no Exterior - Estágio de Pesquisa - Mestrado
Processo FAPESP: 11/04918-7 - Álgebras de Clifford quânticas e álgebras de Hopf associadas
Beneficiário:Ícaro Gonçalves
Linha de fomento: Bolsas no Brasil - Mestrado