Multiloop String-Like Formulas for QED

Abstract

Multiloop gauge-theory amplitudes written in the Feynman-parameter representation are poised to take advantage of two important developments of the last decade: the spinor-helicity technique and the superstring reorganization. The former has been considered in a previous article; the latter will be elaborated in this paper. We show here how to write multiloop string-like formulas in the Feynman-parameter representation for any process in QED, including those involving other non-electromagnetic interactions. The general connection between the Feynman-parameter approach and the superstring/first-quantized approach is discussed. In the special case of a one-loop multi-photon amplitude, these formulas reduce to the ones obtained by the superstring and the first quantized methods. The string-like formulas exhibits a simple gauge structure which makes the Ward-Takahashi identity apparent, and enables the integration-by-parts technique of Bern and Kosower to be applied, so that gauge-invariant parts can be extracted diagram-by-diagram with the seagull vertex neglected.

25 pages in Plain Tex, plus four figures in a postscript file; McGill/92-53

References in corpus (4)

• Multi-Parton Amplitudes in Gauge Theories
• Field Theory Without Feynman Diagrams: One-Loop Effective Actions
• Multiphoton Production at High Energies in the Standard Model I
• Multiphoton Production at High Energies in the Standard Model II

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• Worldline Green Functions for Multiloop Diagrams
• From Free Fields to $AdS$ -- III
• Multiloop Calculations in the String-Inspired Formalism: The Single Spinor-Loop in QED
• From Free Fields to AdS -- II
• Second Order Fermions in Gauge Theories
• On the string-inspired approach to QED in external field
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• DIAGRAMMATIC ANALYSIS OF QCD GAUGE TRANSFORMATIONS AND GAUGE CANCELLATIONS
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• Generalized Background-Field Method
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