Skip to main content
SpringerLink
Log in

Particle Trajectories for Quantum Field Theory

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The formulation of quantum mechanics developed by Bohm, which can generate well-defined trajectories for the underlying particles in the theory, can equally well be applied to relativistic quantum field theories to generate dynamics for the underlying fields. However, it does not produce trajectories for the particles associated with these fields. Bell has shown that an extension of Bohm’s approach can be used to provide dynamics for the fermionic occupation numbers in a relativistic quantum field theory. In the present paper, Bell’s formulation is adopted and elaborated on, with a full account of all technical detail required to apply his approach to a bosonic quantum field theory on a lattice. This allows an explicit computation of (stochastic) trajectories for massive and massless particles in this theory. Also particle creation and annihilation, and their impact on particle propagation, is illustrated using this model.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics, p. 173. Cambridge University Press, Cambridge (1987)

    MATH  Google Scholar 

  2. de Broglie, L.: Tentative d’Interpretation Causale et Non-linéaire de la Mécanique Ondulatoire. Gauthier-Villars, Paris (1956)

    MATH  Google Scholar 

  3. Bohm, D.: Phys. Rev. 85(166), 180 (1952)

    Article  ADS  Google Scholar 

  4. Bohm, D., Hiley, B.J.: The Undivided Universe. Routledge Publ., London (1993)

    MATH  Google Scholar 

  5. Leavens, C.R.: Found. Phys. 25, 229 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  6. Bittner, E.R.: Quantum tunneling dynamics using hydrodynamic trajectories, arXiv:quant-ph/0001119

  7. Vink, J.C.: Nucl. Phys. B 369, 7007 (1992)

    Article  MathSciNet  Google Scholar 

  8. Kowalski-Glikman, J., Vink, J.C.: Class. Quantum Grav. 7, 901 (1990)

    Article  ADS  Google Scholar 

  9. Everett, H.: Rev. Modern Phys. 29, 454 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  10. Wheeler, J.A.: Rev. Modern Phys. 29, 463 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  11. Wyatt, R.E.: Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics. Springer, New York (2005)

    MATH  Google Scholar 

  12. Hughes, K.H., Wyatt, R.E.: Phys. Chem. Chem. Phys. 5, 3905 (2003)

    Article  Google Scholar 

  13. Poirier, B.: J. Chem. Phys. 121, 4501 (2004)

    Article  ADS  Google Scholar 

  14. Trahan, C., Wyatt, R.E., Poirier, B.: J. Chem. Phys. 122: 164104 (2005).

  15. Poirier, B.: Chem. Phys. 370, 4 (2010)

    Article  ADS  Google Scholar 

  16. Vink, J.C.: arXiv:1503.04868 [quant-ph]

  17. Struyve, W.: arXiv:1101.5819 [quant-ph]

  18. Dürr, D., Goldstein, S., Tumulka, R., Zanghí, N.: J. Phys. A 36, 4143 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  19. Dürr, D., Goldstein, S., Tumulka, R., Zanghí, N.: Phys. Rev. Lett. 93, 090402 (2004)

    Article  MathSciNet  Google Scholar 

  20. Dürr, D., Goldstein, S., Zanghì, N.: Bohmian Mechanics and Quantum Theory: An Appraisal. Kluwer Academic Publ, Dordrecht (1996)

    MATH  Google Scholar 

  21. Dürr, D., Goldstein, S., Zanghì, N.: J. Stat. Phys. 67, 843 (1992)

    Article  ADS  Google Scholar 

  22. Goldstein, S., Struyve, W.: J. Stat. Phys. 128, 1197 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  23. Vink, J.C.: Phys. Rev. A 48, 1808 (1993)

    Article  ADS  Google Scholar 

  24. Smit, J.: Introduction to Quantum Fields on a Lattice. Cambridge University Press, Cambridge (2002)

    Book  MATH  Google Scholar 

  25. Montvay, I., Münster, G.: Quantum Fields on a Lattice. Cambridge University Press, Cambridge (1994)

    Book  Google Scholar 

  26. Dürr, D., Goldstein, S., Norsen, T., Struyve, W., Zanghì, N.: arXiv:1307.1714 [quant-ph]

Download references

Author information

Authors and Affiliations

  1. Shell Global Solutions International B.V., Kesslerpark 1, 2288GS, Rijswijk, The Netherlands

    Jeroen C. Vink

Authors
  1. Jeroen C. Vink
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeroen C. Vink.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vink, J.C. Particle Trajectories for Quantum Field Theory. Found Phys 48, 209–236 (2018). https://doi.org/10.1007/s10701-018-0140-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-018-0140-9

Keywords

Search

Navigation