The derivative expansion of the exact renormalization group

TL;DR

This paper introduces a derivative expansion method for the exact renormalization group to perform non-perturbative calculations in quantum field theory, successfully computing critical exponents and reproducing known solutions in critical phenomena.

Contribution

It presents a novel derivative expansion approach for the exact renormalization group, enabling non-perturbative calculations in quantum field theory.

Findings

Calculated critical exponents for 3D O(N) models

Reproduced some exactly known solutions in critical phenomena

Demonstrated the effectiveness of the approximation scheme

Abstract

We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents for three dimensional O(N) symmetric theory. Finally we discuss how the approximation scheme manages to reproduce some exactly known solutions in critical phenomena.