Integration-by-parts identities from the viewpoint of differential geometry

Abstract

We present a new method to construct integration-by-part (IBP) identities from the viewpoint of differential geometry. Vectors for generating IBP identities are reformulated as differential forms, via Poincaré duality. Using the tools of differential geometry and commutative algebra, we can efficiently find differential forms which generate on-shell IBP relation without doubled propagator. Various $D=4$ two-loop examples are presented.

28 pages, 4 figures, based on the author's talk on Amplitudes 2014, a Claude Itzykson memorial conference

References in corpus (4)

• Full one-loop amplitudes from tree amplitudes
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• Eliminating spurious poles from gauge-theoretic amplitudes
• On the Four-Dimensional Formulation of Dimensionally Regulated Amplitudes

Cited by in corpus (2)

• Symmetries of Feynman integrals and the Integration By Parts method
• Integration-by-parts reductions from the viewpoint of computational algebraic geometry