Skip to main content
SpringerLink
Log in

An Alternative to the Gauge Theoretic Setting

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The standard formulation of quantum gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic quantum theoretical access in the spirit of Wigner’s representation theory shows that there is a fundamental clash between the pointlike localization of zero mass (vector, tensor) potentials and the Hilbert space (positivity, unitarity) structure of QT. The quantization approach has no other way than to stay with pointlike localization and sacrifice the Hilbert space whereas the approach built on the intrinsic quantum concept of modular localization keeps the Hilbert space and trades the conflict creating pointlike generation with the tightest consistent localization: semiinfinite spacelike string localization. Whereas these potentials in the presence of interactions stay quite close to associated pointlike field strengths, the interacting matter fields to which they are coupled bear the brunt of the nonlocal aspect in that they are string-generated in a way which cannot be undone by any differentiation.

The new stringlike approach to gauge theory also revives the idea of a Schwinger-Higgs screening mechanism as a deeper and less metaphoric description of the Higgs spontaneous symmetry breaking and its accompanying tale about “God’s particle” and its mass generation for all the other particles.

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. Jordan, P.: Talks and discussions of the theoretical-physical conference in Kharkov (19–25 May 1929). Phys. Z. XXX, 700–725 (1929)

    Google Scholar 

  2. Schroer, B.: Pascual Jordan’s legacy and the ongoing research in quantum field theory. arXiv:1010.4431

  3. Buchholz, D.: The physical state space of quantum electrodynamics. Commun. Math. Phys. 85, 49 (1982)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Haag, R.: Local Quantum Physics, 2nd edn. Springer, Berlin (1996)

    MATH  Google Scholar 

  5. Bloch, F., Nordsieck, A.: Note on the radiation field of the electron. Phys. Rev. 52, 54 (1937)

    Article  ADS  MATH  Google Scholar 

  6. Yenni, D., Frautschi, S., Suura, H.: The infrared divergence phenomena and high energy processes. Ann. Phys. 13, 370–462 (1961)

    ADS  Google Scholar 

  7. Scharf, G.: Quantum Gauge Theories. Wiley, New York (2001)

    MATH  Google Scholar 

  8. Schroer, B.: Unexplored regions in QFT and the conceptual foundations of the Standard Model. arXiv:1010.4431

  9. Mund, J.: String-localized covariant quantum fields. Prog. Math. 251, 199 (2007). arXiv:hep-th/0502014

    Article  MathSciNet  Google Scholar 

  10. Brunetti, R., Guido, D., Longo, R.: Modular localization and Wigner particles. Rev. Math. Phys. 14, 759 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mund, J., Schroer, B., Yngvason, J.: String-localized quantum fields and modular localization. Commun. Math. Phys. 268, 621 (2006). math-ph/0511042

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Weinberg, S.: The Quantum Theory of Fields I. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  13. Schroer, B.: Studies in History and Philosophy of Modern Physics, vol. 41, p. 104 (2010)

    Google Scholar 

  14. Schroer, B.: Modular localization and the d=1+1 formfactor program. Ann. Phys. 295, 190 (1999)

    MathSciNet  ADS  Google Scholar 

  15. Fassarella, L., Schroer, B.: Wigner particle theory and local quantum physics. J. Phys. A 35, 9123–9164 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Mund, J.: String-localized quantum fields, modular localization, and gauge theories. In: Sidoravicius, V. (ed.) New Trends in Mathematical Physic, Selected Contributions of the XVth Int. Congress on Math. Physics, p. 495. Springer, Dordrecht (2009)

    Chapter  Google Scholar 

  17. Leyland, P., Roberts, J., Testard, D.: Duality for quantum free fields. C.N.R.S. preprint July 1978, unpublished

  18. Weinberg, S.: Feynman rules for any spin. Phys. Rev. B 133, 1318 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  19. Joffe, B.L., Fadin, V.S., Lipatov, L.N.: Quantum Chromodynamics. Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology. Cambridge University Press, Cambridge (2010)

    Google Scholar 

  20. Buchholz, D.: Collision theory for massless bosons. Commun. Math. Phys. 52, 147 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  21. Buchholz, D., Fredenhagen, K.: Locality and the structure of particle states. Commun. Math. Phys. 84, 1 (1982)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Steinmann, O.: A new look at the Higgs-Kibble model. arXiv:0804.2989

  23. Schroer, B.: Jorge A. Swieca’s contributions to quantum field theory in the 60s and 70s and their relevance in present research. Eur. Phys. J. H 35, 53 (2010). arXiv:0712.0371

    Article  Google Scholar 

  24. Swieca, J.A.: Charge screening and mass spectrum. Phys. Rev. D 13, 312 (1976)

    Article  ADS  Google Scholar 

  25. Duetsch, M., Schroer, B.: Massive vector mesons and gauge theory. J. Phys. A 33, 4317 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Dütsch, M., Gracia-Bondia, J.M., Scheck, F., Varilly, J.C.: Quantum gauge models without classical Higgs mechanism. arXiv:1001.0932

  27. Lowenstein, J.H., Schroer, B.: Gauge invariance and Ward Identity in a massive Vector Meson Model. Phys. Rev. D 6, 1553 (1972)

    Article  ADS  Google Scholar 

  28. Mund, J., Schroer, B.: work in progress

Download references

Author information

Authors and Affiliations

  1. CBPF, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil

    Bert Schroer

  2. Institut fuer Theoretische Physik der FU Berlin, Berlin, Germany

    Bert Schroer

Authors
  1. Bert Schroer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bert Schroer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schroer, B. An Alternative to the Gauge Theoretic Setting. Found Phys 41, 1543–1568 (2011). https://doi.org/10.1007/s10701-011-9567-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-011-9567-y

Keywords

Search

Navigation