Summing Feynman diagrams in the worldline formalism

C Schubert, N Ahmadiniaz, J Edwards, C Lopez-Arcos, MA Lopez-Lopez, CM Mata, J Nicasio

Research output: Contribution to journalConference proceedings published in a journalpeer-review

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Abstract

The worldline formalism shares with string theory the property that it allows one to write down master integrals that effectively combine the contributions of many Feynman diagrams. While at the one-loop level these diagrams differ only by the position of the external legs along a fixed line or loop, at multiloop they generally involve different topologies. Here we summarize various efforts that have been made over the years to exploit this property in a computationally meaningful way. As a first example, we show how to generalize the Landau-Khalatnikov-Fradkin formula for the non-perturbative gauge transformation of the fermion propagator in QED to the general 2n - point case by pure manipulations at the path-integral level. At the parameter-integral level, we show how to integrate out individual photons in the low-energy expansion, and then sketch a recently introduced general framework for the analytical evaluation of such worldline integrals involving a reduction to quantum mechanics on the circle and the relation between inverse derivatives and Bernoulli polynomials.
Original languageEnglish
Number of pages0
JournalProceedings of Loops and Legs in Quantum Field Theory — PoS(LL2022)
Volume0
Issue number0
Early online date20 Oct 2022
DOIs
Publication statusPublished - 20 Oct 2022
EventLoops and Legs in Quantum Field Theory -
Duration: 25 Apr 2022 → …

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