Contraction of Dirac matrices via chord diagrams. (English) Zbl 1454.81092
Summary: 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.
MSC:
| 81Q30 | Feynman integrals and graphs; applications of algebraic topology and algebraic geometry |
| 81T18 | Feynman diagrams |
| 05C31 | Graph polynomials |
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 15A66 | Clifford algebras, spinors |
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