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Oliver Consa
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The calculation of the electron g-factor was carried out in 1950 by Karplus and Kroll. Seven years later, Petermann detected and corrected a serious error in the calculation of a Feynman diagram. Although it is hard to believe, neither the original calculation nor the subsequent correction was ever published. Therefore, the entire prestige of QED and the Standard Model depends on the calculation of a single Feynman diagram (IIc) that has never been published and cannot be independently verified. In this article we begin the search for any published recalculation of this Feynman diagram IIc that allows us to independently validate the theoretical calculation.
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This year is the 100th birth anniversary of Richard Philips Feynman. This article commemorates his scientific contributions and lasting legacy.
The Symmetries of Feynman Integrals (SFI) is a method for evaluating Feynman Integrals which exposes a novel continuous group associated with the diagram which depends only on its topology and acts on its parameters. Using this method we study the kite diagram, a two-loop diagram with two external legs, with arbitrary masses and spacetime dimension. Generically, this method reduces a Feynman integral into a line integral over simpler diagrams. We identify a locus in parameter space where the integral further reduces to a mere linear combination of simpler diagrams, thereby maximally generalizing the known massless case.
We describe the application of differential reduction algorithms for Feynman Diagram calculation. We illustrate the procedure in the context of generalized hypergeometric functions, and give an example for a type of q-loop bubble diagram.
We study the most general triangle diagram through the Symmetries of Feynman Integrals (SFI) approach. The SFI equation system is obtained and presented in a simple basis. The system is solved providing a novel derivation of an essentially known expression. We stress a description of the underlying geometry in terms of the Distance Geometry of a tetrahedron discussed by Davydychev-Delbourgo [1], a tetrahedron which is the dual on-shell diagram. In addition, the singular locus is identified and the diagrams value on the locuss two components is expressed as a linear combination of descendant bubble diagrams. The massless triangle and the associated magic connection are revisited.
The Symmetries of Feynman Integrals method (SFI) associates a natural Lie group with any diagram, depending only on its topology. The group acts on parameter space and the method determines the integrals dependence within group orbits. This paper analyzes the two-loop vacuum diagram. It is shown how the solution of the SFI equations practically reproduces the most general value of the integral. On the way certain novel derivations are found, a geometrical interpretation is described, and divergences in general dimension are analyzed. These would hopefully be useful for engaging with more involved diagrams.
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