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Annales de l’Institut Henri Poincaré D

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Volume 7, Issue 4, 2020, pp. 457–492
DOI: 10.4171/AIHPD/89

Published online: 2020-09-03

Contraction of Dirac matrices via chord diagrams

Marcel Golz[1]

(1) Humboldt-Universität zu Berlin, Germany

Chord diagrams and combinatorics of word algebras are used to model products of Diracmatrices, their traces, and contractions. A simple formula for the result of arbitrary contractions is derived, simplifying and extending an old contraction algorithm due to Kahane. This formula is then used to express the Schwinger parametric integrand of a QED Feynman integral in a much simplified form, with the entire internal tensor structure eliminated. Possible next steps for further simplification, including a specific conjecture, are discussed.

Keywords: Chord diagrams, Dirac matrices, Feynman integrals, quantum electrodynamics

Golz Marcel: Contraction of Dirac matrices via chord diagrams. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 7 (2020), 457-492. doi: 10.4171/AIHPD/89