Skip to main content
SpringerLink
Log in

Discrete Versions of Some Dirac Type Equations and Plane Wave Solutions

  • Conference paper
  • First Online:
Book cover Differential and Difference Equations with Applications (ICDDEA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 230))

Abstract

A discrete version of the plane wave solution to some discrete Dirac type equations in the spacetime algebra is established. The conditions under which a discrete analogue of the plane wave solution satisfies the discrete Hestenes equation are briefly discussed.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
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

References

  1. Baylis, W.E. (ed.): Clifford (Geometric) Algebra with Applications to Physics, Mathematics, and Engineering. Birkhäuser, Boston (1996)

    MATH  Google Scholar 

  2. Baylis, W.E.: Comment on Dirac theory in spacetime algebra. J. Phys. A Math. Gen. 35, 4791–4796 (2002)

    Article  Google Scholar 

  3. Dezin, A.A.: Multidimensional Analysis and Discrete Models. CRC Press, Boca Raton (1995)

    MATH  Google Scholar 

  4. Hestenes, D.: Real spinor fields. J. Math. Phys. 8(4), 798–808 (1967)

    Article  Google Scholar 

  5. Hestenes, D.: Spacetime Algebra. Gordon and Breach, New York (1966)

    MATH  Google Scholar 

  6. Joyce, W.P.: Dirac theory in spacetime algebra: I. The generalized bivector Dirac equation. J. Phys. A Math. Gen. 34, 1991–2005 (2001)

    Article  MathSciNet  Google Scholar 

  7. Kähler, E.: Der innere differentialkül. Rendiconti di Matematica 21(3–4), 425–523 (1962)

    Google Scholar 

  8. Rabin, J.M.: Homology theory of lattice fermion doubling. Nucl. Phys. B 201(2), 315–332 (1982)

    Article  MathSciNet  Google Scholar 

  9. Sushch, V.: A discrete model of the Dirac–Kähler equation. Rep. Math. Phys. 73(1), 109–125 (2014)

    Article  MathSciNet  Google Scholar 

  10. Sushch, V.: On the chirality of a discrete Dirac–Kähler equation. Rep. Math. Phys. 76(2), 179–196 (2015)

    Article  MathSciNet  Google Scholar 

  11. Sushch, V.: Discrete Dirac–Kähler equation and its formulation in algebraic form. Pliska Stud. Math. 26, 225–238 (2016)

    MathSciNet  MATH  Google Scholar 

  12. Sushch, V.: Discrete Dirac–Kähler and Hestenes equations. Springer Proc. Math. Stat. 164, 433–442 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Koszalin University of Technology, Sniadeckich 2, 75-453, Koszalin, Poland

    Volodymyr Sushch

Authors
  1. Volodymyr Sushch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Volodymyr Sushch .

Editor information

Editors and Affiliations

  1. Departamento de Ciências Exactas e Engenharia, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain

    Tomás Caraballo

  3. Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  4. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, Tennessee, USA

    John R. Graef

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sushch, V. (2018). Discrete Versions of Some Dirac Type Equations and Plane Wave Solutions. In: Pinelas, S., Caraballo, T., Kloeden, P., Graef, J. (eds) Differential and Difference Equations with Applications. ICDDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 230. Springer, Cham. https://doi.org/10.1007/978-3-319-75647-9_37

Download citation

Publish with us

Policies and ethics

Search

Navigation