Structures of spinors fiber bundles with special relativity of Dirac operator using the Clifford algebra

• Autorzy: Hassan Yousif Atyeib Ibrahim

Identyfikatory

URI

10.1515/dema-2021-0035

• Języki publikacji: EN

Abstrakty

EN

The purpose of this article is to demonstrate how to use the mathematics of spinor bundles and their category. We have used the methods of principle fiber bundles obey thorough solid harmonic treatment of pseudo-Riemannian manifolds and spinor structures with Clifford algebras, which couple with Dirac operator to study important applications in cohomology theory.

Słowa kluczowe

EN

Clifford algebra; spinor bundles; principle bundle; spin structure; Dirac operator

PL

algebra Clifforda; spinory; wiązki włókien; struktury; równanie Diraca

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 410--424
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Hassan Yousif Atyeib Ibrahim

• Department of Mathematics, College of Science and Arts, Qassim University, ArRass, Kingdom of Saudi Arabia

Bibliografia

• [1] J. J. Venselaar, Spinors and Dirac Operators, Caltech, California, USA, 2007.
• [2] H. B. Lawson and M.-L. Michelsohn, Spin Geometry, Princeton University, New Jersey, USA, 1989.
• [3] H. Schröder, On the definition of geometric Dirac operators, https://arxiv.org/abs/math/0005239, (2000).
• [4] J. M. Bismut, Introduction to the Index Theory, University of Paris, France, 1986.
• [5] A. R. Mosona and A. W. Rodrigues, The Fundle of Algebraic and Dirac-Hestenes Spinor Field, 13083-970 Campinas, SP Brazil, 2004.
• [6] S. Morrison, Classifying spinor structures, Master’s thesis, University of New South Wales, https://arxiv.org/abs/math-ph/0106007, (2001).
• [7] N. Steenrod, The Topology of Fibre Bundles, Princeton University, USA, 1999.
• [8] K. Wernli, Lecture notes on spin geometry, arXiv:1911.09766v1, (2019).
• [9] L. Claessens, Field theory from a bundle point of view, Belgium, 2011, https://www.yumpu.com/en/document/view/33648732/field-theory-from-a-bundle-point-of-view.
• [10] J. L. Koszul, Lectures on Fibre Bundles and Differential Geometry, Bombay, 1960.
• [11] G. Ottaviani, Spinor bundles on quadrics, Trans. Amer. Math. Soc. 307 (1988), no. 1, 301-316.
• [12] A. Trautman, Connections and the Dirac operator on spinor bundles, J. Geom. Phys. 58 (2007), 238-252.
• [13] C. Kassel, Homology and Cohomology of Associative Algebras, Notes in the Advanced School on Non-commutative Geometry at ICTP, Trieste, Italy, 2004.
• [14] T. Friederish and A. Trautman, Clifford Structures and Spinor Bundles, Berlin, Germany and Warsaw, Poland, 1997.
• [15] M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology 3 (1964), 3-38.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).