Feynman Integral Calculus

• Main Author: Smirnov, Vladimir A. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Subjects: Physics.; Mathematical analysis.; Analysis (Mathematics).; Quantum physics.; Elementary particles (Physics).; Quantum field theory.; Elementary Particles, Quantum Field Theory.; Analysis.; Quantum Physics.

The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. `Feynman Integral Cal...

Table of Contents:

• Feynman Integrals: Basic Definitions and Tools
• Evaluating by Alpha and Feynman Parameters
• Evaluating by MB Representation
• IBP and Reduction to Master Integrals
• Reduction to Master Integrals by Baikov’s Method
• Evaluation by Differential Equations
• Tables
• Some Special Functions
• Summation Formulae
• Table of MB Integrals
• Analysis of Convergence and Sector Decompositions
• A Brief Review of Some Other Methods
• Applying Gröbner Bases to Solve IBP Relations
• Solutions.