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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Gupta, S. N.: Proc. Soc. (London)63, 681 (1950)
Bleuler, K. T.: Helv. Phys. Acta23, 567 (1950)
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
Streater, R., Wightman, A. S.: PCT, Spin and statistics and all that. New York: Benjamin 1964
Strocchi, F.: Phys. Rev.162, 1429 (1967)
Strocchi, F.: Phys. Rev. D2, 2334 (1970)
Kastler, D., Robinson, D. W., Swieca, A.: Commun. math. Phys.2, 108 (1966)
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]
For a discussion of the properties ofH in the free field case see Wightman, A. S., Gårding, L.: Arkiv Fysik28, 129 (1964)
Author information
Authors and Affiliations
Additional information
Research supported by AFOSR, Contract F 44620-71-C-0108
Rights 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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01646452