Skip to main content
SpringerLink
Log in

Covariant canonical quantization of fields and Bohmian mechanics

  • Theoretical Physics
  • Published:
The European Physical Journal C - Particles and Fields Aims and scope Submit manuscript

Abstract.

We propose a manifestly covariant canonical method of field quantization based on the classical De Donder-Weyl covariant canonical formulation of field theory. Owing to covariance, the space and time arguments of fields are treated on an equal footing. To achieve both covariance and consistency with standard non-covariant canonical quantization of fields in Minkowski spacetime, it is necessary to adopt a covariant Bohmian formulation of quantum field theory. A preferred foliation of spacetime emerges dynamically owing to a purely quantum effect. The application to a simple time-reparametrization invariant system and quantum gravity is discussed and compared with the conventional non-covariant Wheeler-DeWitt approach.

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.B. Green, J.H. Schwarz, E. Witten, Superstring theory (Cambridge University Press, Cambridge 1987)

  2. M. Gaul, C. Rovelli, Lect. Notes Phys. 541, 277 (2000)

    Google Scholar 

  3. T. Thiemann, Lect. Notes Phys. 631, 41 (2003)

    Google Scholar 

  4. C. Rovelli, Quantum gravity (Cambridge University Press, Cambridge 2004); http://www.cpt.univ-mrs.fr/\( \tilde{} \)rovelli

  5. T. Banks, W. Fischler, S.H. Shenker, L. Suskind, Phys. Rev. D 55, 5112 (1997)

    Article  Google Scholar 

  6. Č. Crnković, E. Witten, in Three Hundred Years of Gravitation, edited by S.W. Hawking, W. Israel (Cambridge University Press, Cambridge 1987)

  7. Č. Crnković, Class. Quant. Grav. 5, 1557 (1988)

    Article  Google Scholar 

  8. H.A. Kastrup, Phys. Rep. 101, 1 (1983)

    Article  Google Scholar 

  9. M.J. Gotay, J. Isenberg, J.E. Marsden, physics/9801019

  10. C. Rovelli, gr-qc/0207043

  11. I.V. Kanatchikov, Phys. Lett. A 283, 25 (2001)

    Article  Google Scholar 

  12. I.V. Kanatchikov, Int. J. Theor. Phys. 40, 1121 (2001)

    Article  Google Scholar 

  13. D. Bohm, Phys. Rev. 85, 180 (1952)

    Article  Google Scholar 

  14. D. Bohm, B.J. Hiley, P.N. Kaloyerou, Phys. Rep. 144, 349 (1987)

    Article  Google Scholar 

  15. P.R. Holland, Phys. Rep. 224, 95 (1993)

    Article  Google Scholar 

  16. P.R. Holland, The quantum theory of motion (Cambridge University Press, Cambridge 1993)

  17. D.F. Styer et al. , Am. J. Phys. 70, 288 (2002)

    Article  Google Scholar 

  18. H. Nikolić, quant-ph/0307179

  19. H. Nikolić, quant-ph/0406173, to appear in Found. Phys. Lett.

  20. J.A. deBarros, N. Pinto-Neto, M.A. Sagioro-Leal, Phys. Lett. A 241, 229 (1998)

    Article  Google Scholar 

  21. R. Colistete Jr., J.C. Fabris, N. Pinto-Neto, Phys. Rev. D 57, 4707 (1998)

    Article  Google Scholar 

  22. N. Pinto-Neto, R. Colistete Jr., Phys. Lett. A 290, 219 (2001)

    Article  Google Scholar 

  23. J. Marto, P.V. Moniz, Phys. Rev. D 65, 023516 (2001)

    Article  Google Scholar 

  24. N. Pinto-Neto, E.S. Santini, Phys. Lett. A 315, 36 (2003)

    Article  Google Scholar 

  25. G.D. Barbosa, N. Pinto-Neto, Phys. Rev. D 69, 065014 (2004)

    Article  Google Scholar 

  26. J. von Rieth, J. Math. Phys. 25, 1102 (1984)

    Article  Google Scholar 

  27. A. Valentini, Phys. Lett. A 156, 5 (1991)

    Article  Google Scholar 

  28. P. Hořava, Class. Quant. Grav. 8, 2069 (1991)

    Article  Google Scholar 

  29. I.V. Kanatchikov, Rep. Math. Phys. 53, 181 (2004)

    Article  Google Scholar 

  30. K. Kuchař, in Relativity, Astrophysics, and Cosmology, edited by W. Israel (Reidel Publishing Company, Dordrecht/Boston 1973)

  31. T. Padmanabhan, Int. J. Mod. Phys. A 4, 4735 (1989)

    Article  Google Scholar 

  32. K. Kuchař, in Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics (World Scientific, Singapore 1992)

  33. C.J. Isham, gr-qc/9210011

  34. J.D.E. Grant, I.G. Moss, Phys. Rev. D 56, 6284 (1997)

    Article  Google Scholar 

  35. T. Padmanabhan, Phys. Rep. 406, 49 (2005)

    Article  MathSciNet  Google Scholar 

  36. A. Shojai, F. Shojai, Class. Quant. Grav. 21, 1 (2004)

    Article  Google Scholar 

  37. G. Esposito, G. Gionti, C. Stornaiolo, Nuovo Cim. B 110, 1137 (1995)

    Google Scholar 

  38. G. Horton, C. Dewdney, J. Phys. A 37, 11935 (2004)

    Google Scholar 

  39. N.D. Birrell, P.C.W. Davies, Quantum fields in curved space (Cambridge Press, New York 1982)

Download references

Author information

Authors and Affiliations

  1. Theoretical Physics Division, Rudjer Bošković Institute, P.O.B. 180, 10002, Zagreb, Croatia

    H. Nikolić

Authors
  1. H. Nikolić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Nikolić.

Additional information

Received: 11 October 2004, Published online: 6 July 2005

PACS:

04.20.Fy, 04.60.Ds, 04.60.Gw, 04.60.-m

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nikolić, H. Covariant canonical quantization of fields and Bohmian mechanics. Eur. Phys. J. C 42, 365–374 (2005). https://doi.org/10.1140/epjc/s2005-02296-7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s2005-02296-7

Keywords

Search

Navigation