Perturbative Calculation of Multi-Loop Feynman Diagrams. New Type of Expansions for Critical Exponents

TL;DR

This paper introduces a novel method for calculating multi-loop Feynman integrals in quantum field theory, enabling exact computation of critical exponents in three dimensions through a matrix multiplication approach.

Contribution

It presents a new expansion technique that simplifies multi-loop Feynman diagram calculations and allows for exact determination of critical exponents.

Findings

Calculation of L-loop integrals reduced to matrix multiplications

Exact coefficients for critical exponents in three dimensions obtained

New expansion method enhances precision in quantum field theory computations

Abstract

We show that the calculation of L-loop Feynman integrals in D dimensions can be reduced to a series of matrix multiplications in D times L dimensions. This gives rise to a new type of expansions for the critical exponents in three dimensions in which all coefficients can be calculated exactly.