Clifford algebras and classification of spinors from the bilinear covariants
Fluid/gravity correspondence, fermionic sectors and its ramifications
| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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
Total Affiliations: 4
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| Document type: | Journal article |
| Source: | Journal of Mathematical Physics; v. 55, n. 10 OCT 2014. |
| Web of Science Citations: | 21 |
| Abstract | |
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) | |
| FAPESP's process: | 11/04918-7 - Quantum Clifford algebras and associated Hopf algebras |
| Grantee: | Ícaro Gonçalves |
| Support Opportunities: | Scholarships in Brazil - Master |
| FAPESP's process: | 12/07710-0 - Classical groups in the Quantum Clifford algebras formalism |
| Grantee: | Ícaro Gonçalves |
| Support Opportunities: | Scholarships abroad - Research Internship - Master's degree |