Skip to main content
SpringerLink
Log in

Huygens’ principle and Dirac-Weyl equation

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

We investigate the validity of Huygens’ principle for forward propagation in the massless Dirac-Weyl equation. The principle holds for odd space dimension n, while it is invalid for even n. We explicitly solve the cases \(n = 1, 2\) and 3 and discuss generic n. We compare with the massless Klein-Gordon equation and comment on possible generalizations and applications.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Born, E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999)

  2. J. Hadamard, Lectures on Cauchy’s Problem in Linear Partial Differential Equations (Dover Publications, New York, 1923)

  3. E.C. Zachmanoglou, D.W. Thoe, Introduction to Partial Differential Equations with Applications (Dover Publications, New York, 1986)

  4. L.C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, Vol. 19 (American Mathematical Society, Providence, Rhode Island, 2001)

  5. P. Günther, Huygens’ principle and hyperbolic equations (Academic Press, San Diego, 1988)

  6. F.A.C.C. Chalub, J.P. Zubelli, J. Nonlinear Math. Phys. 8, 62 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  7. F.A.C.C. Chalub, J.P. Zubelli, Cont. Math. AMS 362, 89 (2004)

    Article  Google Scholar 

  8. M.E. Peskin, D.V. Schroeder, An introduction to Quantum Field Theory (Perseus Books, Reading, 1995)

  9. R.P. Feynman, Quantum Electrodynamics (W. A. Benjamin, New York, 1961)

  10. A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)

    Article  ADS  Google Scholar 

  11. M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nat. Phys. 2, 620 (2006)

    Article  Google Scholar 

  12. E. Zohar, J.I. Cirac, B. Reznik, Phys. Rev. Lett. 109, 125302 (2012)

    Article  ADS  Google Scholar 

  13. D. Banerjee, M. Dalmonte, M. Müller, E. Rico, P. Stebler, U.-J. Wiese, P. Zoller, Phys. Rev. Lett. 109, 175302 (2012)

    Article  ADS  Google Scholar 

  14. S. Notarnicola, E. Ercolessi, P. Facchi, G. Marmo, S. Pascazio, F.V. Pepe, J. Phys. A: Math. Theor. 48, 30FT01 (2015)

    Article  Google Scholar 

  15. T. Pichler, M. Dalmonte, E. Rico, P. Zoller, S. Montangero, Phys. Rev. X 6, 011023 (2016)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica and MECENAS, Università di Bari, I-70126, Bari, Italy

    Saverio Pascazio

  2. INFN, Sezione di Bari, I-70126, Bari, Italy

    Saverio Pascazio & Francesco V. Pepe

  3. Istituto Nazionale di Ottica (INO-CNR), I-50125, Firenze, Italy

    Saverio Pascazio

  4. Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, I-00184, Roma, Italy

    Francesco V. Pepe

  5. Universidad Carlos III de Madrid, 28911, Madrid, Spain

    Juan Manuel Pérez-Pardo

Authors
  1. Saverio Pascazio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesco V. Pepe
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Juan Manuel Pérez-Pardo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saverio Pascazio.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pascazio, S., Pepe, F.V. & Pérez-Pardo, J.M. Huygens’ principle and Dirac-Weyl equation. Eur. Phys. J. Plus 132, 287 (2017). https://doi.org/10.1140/epjp/i2017-11593-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2017-11593-6

Search

Navigation