High-order perturbative expansions of multi-parameter Phi^4 quantum field theories

TL;DR

This paper develops high-order perturbative expansions for complex multi-parameter Phi^4 quantum field theories, enabling detailed analysis of their symmetry breaking patterns and physical properties.

Contribution

It provides the first five- or six-loop perturbative series for several multi-parameter Phi^4 models, extending previous work on simpler theories.

Findings

High-order series up to six loops for multi-parameter Phi^4 theories.

Explicit series for O(M)×O(N)-symmetric and spin-density-wave models.

Facilitates advanced theoretical analysis of complex symmetry breaking.

Abstract

We present high-order pertubative expansions of multi-parameter Phi^4 quantum field theories with an N-component fundamental field, containing up to 4th-order polynomials of the field. Multi-parameter Phi^4 theories generalize the simplest O(N)-symmetric Phi^4 theories, and describe more complicated symmetry breaking patterns. These notes collect several high-order perturbative series of physically interesting multi-parameter Phi^4 theories, to five or six loops. We consider the O(M)XO(N)-symmetric Phi^4 model, the so-called MN model, and a spin-density-wave Phi^4 model containing five quartic terms.