Banana integrals in configuration space
Sergio L. Cacciatori, Henri Epstein, Ugo Moschella
Abstract
We reconsider the computation of banana integrals at different loops, by working in the configuration space, in any dimension. We show how the 2-loop banana integral can be computed directly from the configuration space representation, without the need to resort to differential equations, and we include the analytic extension of the diagram in the space of complex masses. We also determine explicitly the ε expansion of the two loop banana integrals, for d=j−2ε, j=2,3,4.
Topics & Concepts
Configuration spaceSpace (punctuation)Extension (predicate logic)Representation (politics)Loop (graph theory)DiagramComputationDimension (graph theory)MathematicsDifferential (mechanical device)Loop spaceMathematical analysisPure mathematicsAlgebra over a fieldTopology (electrical circuits)PhysicsComputer scienceCombinatoricsAlgorithmQuantum mechanicsProgramming languageStatisticsLawOperating systemPoliticsThermodynamicsPolitical scienceBlack Holes and Theoretical PhysicsAdvanced Topics in AlgebraCosmology and Gravitation Theories