Bubble diagram through the Symmetries of Feynman Integrals method

Abstract

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 integral's dependence within group orbits. This paper analyzes the bubble diagram, namely the 1-loop propagator diagram, through the SFI method. This is the first diagram with external legs to be analyzed within SFI, and the method is generalized to include this case. The set of differential equation is obtained. In order to solve it the set is transformed into partially invariants variables. The equations are integrated to reproduce the integral's value. This value is interpreted in terms of triangle geometry suggested by extant papers.

24 pages, 4 figures. v2: Full version replacing an announcement version. Abstract essentially unchanged. v3: Singular locus corrected

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Cited by in corpus (6)

• The propagator seagull: general evaluation of a two loop diagram
• The vacuum seagull: evaluating a 3-loop Feynman diagram with 3 mass scales
• Two-loop vacuum diagram through the Symmetries of Feynman Integrals method
• A Feynman integral in Lifshitz-point and Lorentz-violating theories in $R^D\oplus R^m$
• Kite diagram through Symmetries of Feynman Integrals
• Algebraic aspects of when and how a Feynman diagram reduces to simpler ones