INTEGRATION BY PARTS: AN INTRODUCTION

2011/04/30 by Andrey Grozin, A. G. Grozin
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Classical mechanics #Feynman diagram #Feynman integral #Geometry #Integration by parts #Mathematical analysis #Mathematical physics #Numerical integration #Order of integration (calculus) #Particle physics theoretical and experimental studies #Physics #Scalar (mathematics) #Theoretical physics #hep-ph

paper · pdf · doi:10.1142/s0217751x11053687

published as Int.J.Mod.Phys.A26:2807-2854,2011 · Lectures at CAPP-2011 (Zeuthen), 47 p; v2: small improvements, references added; v3: small improvements, 1 reference added; v4: a few typos in formulas fixed

openalex publication_date 2011/05/31 · arxiv created 2011/06/28 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Integration by parts is used to reduce scalar Feynman integrals to master integrals.

Citations

• Explicit solutions of the multi-loop integral recurrence relations and its application
• Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals
• Integration by parts: The algorithm to calculate β-functions in 4 loops
• The number of master integrals is finite
• Recurrence relations for three-loop prototypes of bubble diagrams with a mass
• Differential Equations for Two-Loop Four-Point Functions
• Explicit solutions of the 3-loop vacuum integral recurrence relations
• Connection between Feynman integrals having different values of the space-time dimension
• Space–time dimensionality D as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D