Abstract
In this paper, some relationships between spinor and vector fields are investigated in detail, with the aid of computer algebra (calculations have been performed with MAPLE). In particular, an exact paradigm based on the representations of vector spaces is shown, strictly linking Pauli spinor fields with 3-dimensional rotations and vector fields. As an application, the problem of a classical particle in a central field of force is described in terms of one 2-component spinor field: the spinor equation of motion resembles the wave equation of quantum mechanics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Ablamowicz, P. Lounesto, J. Maks: 1991, ‘Conference report. Second workshop on “Clifford algebras and their applications in mathematical physics”, Universite des Sciences et Techniques du Languedoc, Montpellier, France, 1989’, Found. Phys. 21, pp. 735–748.
V. B. Berestetskii, E. M. Lifshitz, L. P. Pitayevskii: 1971, Relativistic quantum theory (Part I), Pergamon Press, Oxford.
H. Goldstein: 1980, Classical mechanics 2nd Ed., Addison-Wesley, Reading.
L. D. Landau, E. M. Lifshitz: 1958, Quantum mechanics (non-relativistic theory), Pergamon Press, Oxford.
R. Penrose: 1983, ‘Spinors and torsion in general relativity’, Found. Phys. 13, pp. 325–339.
F. Piazzese: 1992, ‘On the classical theory of elementary spinors’, in M. Goldberg, D. Hershkowitz, H. Schneider (eds.): Report on “Sixth Haifa Conference on Matrix Theory”, Haifa, Israel, 1990, Lin. Alg. Appl. 167, pp. 242–247.
F. Piazzese: 1993a, ‘2− and 4-component spinors. What, in fact are they?’, J. Natural Geometry 3, pp. 59–79.
F. Piazzese: 1993b, ‘The “ideal” approach to spinors reconsidered’, in F. Brackx, R. Delanghe, H. Serras (eds.): Proceedings of the Third Conference on “Clifford Algebras and their Applications in Mathematical Physics”, Deinze, Belgium, 1993, Kluwer, Dordrecht, pp. 325–332.
E. Persico: 1950, Fundamentals of quantum mechanics, Prentice-Hall, Englewood Cliffs.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Birkhäuser Boston
About this chapter
Cite this chapter
Piazzese, F. (1996). Computer Algebra in Spinor Calculations. In: Abłamowicz, R., Parra, J.M., Lounesto, P. (eds) Clifford Algebras with Numeric and Symbolic Computations. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4615-8157-4_9
Download citation
DOI: https://doi.org/10.1007/978-1-4615-8157-4_9
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4615-8159-8
Online ISBN: 978-1-4615-8157-4
eBook Packages: Springer Book Archive