Quantum mechanical path integrals in the first quantised approach to quantum field theory

Abstract

Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation theory. Here we review the history, main features and present applications of the formalism. Our emphasis is on recent developments such as the path integral representation of open fermion lines, the description of colour using auxiliary worldline fields, incorporation of higher spin, and extension of the formalism to non-commutative space.

13 Pages, 3 figures. Technical Report to be published in the proceedings of the workshop "Path Integration in Complex Dynamical Systems," Leiden, 6 Feb - 10 Feb 2017

References in corpus (13)

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• Multidimensional Worldline Instantons
• Gravitational corrections to the Euler-Heisenberg Lagrangian
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• Scalar heat kernel with boundary in the worldline formalism
• U(N) spinning particles and higher spin equations on complex manifolds
• Mixed symmetry Wilson-loop interactions in the worldline formalism
• Heat Trace Asymptotics on Noncommutative Spaces
• The Fermion Content of the Standard Model
• Asymptotic behavior of the QED perturbation series