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Perturbative quantum field theory in the string-inspired formalism. (English) Zbl 0988.81108
Summary: We review the status and present range of applications of the “string-inspired” approach to perturbative quantum field theory. This formalism offers the possibility of computing effective actions and \(S\)-matrix elements in a way which is similar in spirit to string perturbation theory, and bypasses much of the apparatus of standard second-quantized field theory. Its development was initiated by Bern and Kosower, originally with the aim of simplifying the calculation of scattering amplitudes in quantum chromodynamics and quantum gravity. We give a short account of the original derivation of the Bern-Kosower rules from string theory. Strassler’s alternative approach in terms of first-quantized particle path integrals is then used to generalize the formalism to more general field theories, and, in the abelian case, also to higher loop orders. A considerable number of sample calculations are presented in detail, with an emphasis on quantum electrodynamics.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81V10 Electromagnetic interaction; quantum electrodynamics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
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