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Conformal Gauges and Renormalized Equations of Motion in Massless Quantum Electrodynamics

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Quantum Field Theory

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Abstract

A formulation of massless QED is studied with a non-singular Lagrangian and conformal invariant equations of motion. It makes use of non- decomposable representations of the conformal group G and involves two dimensionless scalar fields (in addition to the conventional charged field and electromagnetic potential) but gauge invariant Green functions are shown to coincide with those of standard (massless) QED. Assuming that the (non- elementary) representation of G for the 5-potential which leaves the equations of motion invariant and leads to the free photon propagator of Johnson-Baker- Adler (JBA) conformal QED remains unaltered by renormalization, we prove that consistency requirements for conformal invariant 2-, 3-, and 4-point Green functions satisfying (renormalized) equations of motion and standard Ward identities lead to either a trivial solution (with eψ= 0) or to a subcanonical dimension d=1/2 for the charged field.

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Authors and Affiliations

  1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, BG-1184, Sofia, Bulgaria

    V. B. Petkova, G. M. Sotkov & I. T. Todorov

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  1. V. B. Petkova
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  2. G. M. Sotkov
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  3. I. T. Todorov
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Editors and Affiliations

  1. Department of Physics, Lyman Laboratory of Physics, Harvard University, Cambridge, MA, 02138, USA

    Arthur Jaffe

  2. II. Institut für Theoretische Physik der Universität Hamburg, D-2000, Hamburg 50, Fed. Rep. of Germany

    Harry Lehmann  & Gerhard Mack  & 

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Petkova, V.B., Sotkov, G.M., Todorov, I.T. (1985). Conformal Gauges and Renormalized Equations of Motion in Massless Quantum Electrodynamics. In: Jaffe, A., Lehmann, H., Mack, G. (eds) Quantum Field Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70307-2_14

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  • DOI: https://doi.org/10.1007/978-3-642-70307-2_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15260-6

  • Online ISBN: 978-3-642-70307-2

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