Perturbative formulae for relativistic interactions of effective particles

TL;DR

This paper develops perturbative formulae for relativistic interactions of effective particles within quantum field theory, enabling systematic approximation of the full Hamiltonian through successive perturbative steps.

Contribution

It introduces a set of general 4th-order perturbative formulae for effective particle interactions in relativistic quantum field theories.

Findings

Derived explicit 4th-order perturbative formulae

Provided a framework for initial perturbative analysis of effective interactions

Facilitated systematic construction of effective Hamiltonians

Abstract

The concept of effective particles as degrees of freedom in a relativistic quantum field theory is defined using a non-perturbative renormalization group procedure for Hamiltonians. However, every candidate for a basic physical theory appears to require an initial perturbative search for the set of interaction terms that may provide a basis with which the full effective theory Hamiltonian could be constructed in a series of successive approximations. This article describes the required perturbative expansion and illustrates it with a set of general 4th-order formulae.