Perturbative Quantum Field Theory in the String-Inspired Formalism

TL;DR

This paper reviews the string-inspired formalism for perturbative quantum field theory, highlighting its ability to simplify calculations of effective actions and scattering amplitudes, especially in QED, by using string theory techniques.

Contribution

It introduces a generalized string-inspired approach to quantum field theory calculations, extending Bern-Kosower rules and applying first-quantized path integrals to higher loop orders.

Findings

Simplified calculation methods for QED amplitudes.

Extension of the formalism to higher loop orders.

Numerous detailed sample calculations.

Abstract

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.