Skip to main content

On the Relationships between the Dirac Spinors and Clifford Subalgebra Cl +1,3

  • Chapter
Clifford Algebras and Spinor Structures

Part of the book series: Mathematics and Its Applications ((MAIA,volume 321))

  • 575 Accesses

Abstract

This paper deals with a new algebraic construction making the link between the Dirac spinors (as defined on the basis of the transformation law) and the Clifford subalgebra Cl +1,3 an obvious one.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

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,” Université des Sciences et Techniques du Languedoc, Montpellier, France, 1989’, Found. Phys. 21, 735–748.

    Article  Google Scholar 

  • W. L. Bade, H. Jehle: 1953, ‘An introduction to spinors’, Rev. Mod. Phys. 25, 714–728.

    Article  MathSciNet  MATH  Google Scholar 

  • A. O. Barut: 1964, ‘Electrodynamics and classical theory of fields and particles’, Macmillan, New York.

    Google Scholar 

  • V. B. Berestetskii, E. M. Lifshitz and L. P. Pitayevskii: 1971, ‘Relativistic quantum theory’ Part I, Pergamon, Oxford.

    Google Scholar 

  • A. Crumeyrolle: 1990, ‘Orthogonal and Symplectic Clifford Algebras, Spinor Structures’, Kluwer, Dordrecht.

    Book  MATH  Google Scholar 

  • C.G. Darwin: 1928, ‘The Wave Equations of the Electron’, Proc. Royal Soc. London A 118, 654–680.

    Article  MATH  Google Scholar 

  • F. A. M. Prescura, B. J. Hiley: 1980, ‘The implicate order, algebras,and the spinor’, Found. Phys. 10, 7–31.

    Article  MathSciNet  Google Scholar 

  • H. Goldstein: 1980, ‘Classical mechanics’ 2nd Ed., Addison-Wesley, Reading.

    MATH  Google Scholar 

  • L. Infeld, B. L. Van der Waerden: 1933, Sitber. preuss., Akad. Wiss, Physik.-math. Kl. 380.

    Google Scholar 

  • D. Hestenes: 1971, ‘Vectors, spinors, and complex numbers in classical and quantum physics’, Am. J. Phys. 39, 1013–1027.

    Article  MathSciNet  Google Scholar 

  • D. Hestenes: 1975, ‘Observables, operators, and complex numbers in the Dirac theory’, J. Math. Phys. 16, 1975, 556–572.

    Article  MathSciNet  Google Scholar 

  • R. Kjellander: 1981, ‘A geometrical definition of spinors from ‘orientations’ in three-dimensional space leading to a linear spinor visualization’, J. Phys. A: Math. Gen. 14, 1863–1885.

    Article  MathSciNet  MATH  Google Scholar 

  • P. Lounesto: 1981, ‘Scalar Products of Spinors and an Extension of Brauer-Wall Groups’, Found. Phys. 11, 721–740.

    Article  MathSciNet  Google Scholar 

  • R. Penrose: 1983, ‘Spinors and torsion in general relativity’, Found. Phys. 13, 325–339.

    Article  MathSciNet  Google Scholar 

  • 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, 242–247.

    Google Scholar 

  • F. Piazzese: 1993 a, ‘2- and 4-component spinors. What, in fact are they?’, J. Natural Geometry 3, 59–79.

    MathSciNet  MATH  Google Scholar 

  • F. Piazzese: 1993 b, ‘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.

    Google Scholar 

  • P. Rastall: 1972, ‘A new spinor calculus’, Gen. Rel. Grav. 3, 281–304.

    Article  MathSciNet  MATH  Google Scholar 

  • M. Riesz: 1947 C. R. Dixième Congrès Math. Scandinaves 1946, Copenhagen: Jul. Gjellerup Forlag, 123–148.

    Google Scholar 

  • M. Riesz: 1958, ‘Clifford Numbers and Spinors’, Univ. of Maryland. Facsimile reproduction by Kluwer, 1993.

    MATH  Google Scholar 

  • B.L. Van der Waerden: 1929, Nachr. Akad. Wiss. Gottingen, Math.-physik Kl. 100, translated in English as ‘Spinor Analysis’, in M.Fierz, V.F. Weisskopf (eds.): 1958, Theoretical Physics in the XXth. Century Interscience, New York, page 236.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Piazzese, F. (1995). On the Relationships between the Dirac Spinors and Clifford Subalgebra Cl +1,3 . In: Ablamowicz, R., Lounesto, P. (eds) Clifford Algebras and Spinor Structures. Mathematics and Its Applications, vol 321. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8422-7_10

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-8422-7_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4525-6

  • Online ISBN: 978-94-015-8422-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics