Scattering theory for quantum electrodynamics. I. Infrared renormalization and asymptotic fields

Daniel Zwanziger
Phys. Rev. D 11, 3481 – Published 15 June 1975
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Abstract

The present article lays the theoretical foundation for a scattering theory of quantum electrodynamics, which is completed into a practical calculational scheme in the accompanying article. In order to circumvent infrared divergences, an infrared renormalization procedure is instituted whereby a Lorentz-invariant, but indefinite, inner product is defined for a class of photon test functions defined on the future light cone kμ=ω(1, k^), ω0. This class includes test functions whose low-frequency behavior is given by φμ(k)epμp·k, for which the usual inner product d3k(2ω)1φμ*(k)(gμν)φν(k) is infrared-divergent. The Fock space of such test functions provides a representation space for the asymptotic fields of quantum electrodynamics. It contains subspaces in which the indefinite metric is non-negative which, when completed in the norm, yield physical Hilbert spaces. This Fock space of test functions thereby replaces the nonphysical Hilbert space of the usual Gupta-Bleuler method and its positive-definite but noncovariant metric. As an application the S matrix and finite transition probabilities are found for the bremsstrahlung emitted by the classical external current of a scattered charged particle. A final result is a simple weak asymptotic limit of the charged field ψ. It is used as a starting point in the accompanying article, for the derivation of reduction formulas for the quantum electrodynamical S matrix.

  • Received 24 September 1974

DOI:https://doi.org/10.1103/PhysRevD.11.3481

©1975 American Physical Society

Authors & Affiliations

Daniel Zwanziger*

  • Department of Physics, New York University, New York, New York 10003

  • *Work supported in part by funds from the National Science Foundation under Grant No. GP-36481X.

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Vol. 11, Iss. 12 — 15 June 1975

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