Skip to main content
SpringerLink
Log in

Some remarks on local operators in quantum electrodynamics

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We assume the existence of a conserved current which generates locally gauge transformations of first kind. We are working in a local quantum Field Theory, where the fields are defined on a vector space where indefinite metric is allowed.

We show that the Maxwell equations are not consistent with the above assumptions and the vectors obtained by applying local charged operators on the vacuum cannot describe physical states.

Moreover we show that, if charged fields have non-trivial expectation value on the physical states, the vector space must contain vectors with negative norm.

We discuss the relation between the local formulation of QED and a formulation in terms of physical states. As an example we study the transition from Gupta-Bleuler free QED to the Coulomb-gauge formulation.

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. Gupta, S. N.: Proc. Soc. (London)63, 681 (1950)

    Google Scholar 

  2. Bleuler, K. T.: Helv. Phys. Acta23, 567 (1950)

    Google Scholar 

  3. Dirac, P. A. M.: Proc. Roy. Soc. (London) A114, 243, 710 (1927). The principles of quantum mechanics, 4th ed. Oxford-New York: University Press 1958; J. D. Bjorken and S. D. Drell, Relativistic quantum fields. New York: McGraw-Hill 1965

    Google Scholar 

  4. Streater, R., Wightman, A. S.: PCT, Spin and statistics and all that. New York: Benjamin 1964

    Google Scholar 

  5. Strocchi, F.: Phys. Rev.162, 1429 (1967)

    Google Scholar 

  6. Strocchi, F.: Phys. Rev. D2, 2334 (1970)

    Google Scholar 

  7. Kastler, D., Robinson, D. W., Swieca, A.: Commun. math. Phys.2, 108 (1966)

    Google Scholar 

  8. Schweber, S. S.: An introduction to relativistic quantum field theory. New York: Harper and Row 1964. For a discussion of this problem in axiomatic field theory see, F. Strocchi [4]

    Google Scholar 

  9. For a discussion of the properties ofH in the free field case see Wightman, A. S., Gårding, L.: Arkiv Fysik28, 129 (1964)

    Google Scholar 

Download references

Author information

Author notes

  1. F. Strocchi

    Present address: Istituto Nazionale de Fisica Nucleare, Sezione di Pisa, Pisa, Italy

Authors and Affiliations

  1. Istituto di Fisica dell'Universitá, Pisa

    R. Ferrari & L. E. Picasso

  2. Istituto Nazionale de Fisica Nucleare, Sezione di Pisa, Pisa, Italy

    R. Ferrari & L. E. Picasso

  3. Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey, USA

    F. Strocchi

Authors
  1. R. Ferrari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. E. Picasso
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Strocchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by AFOSR, Contract F 44620-71-C-0108

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ferrari, R., Picasso, L.E. & Strocchi, F. Some remarks on local operators in quantum electrodynamics. Commun.Math. Phys. 35, 25–38 (1974). https://doi.org/10.1007/BF01646452

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01646452

Keywords

Search

Navigation