On the Nonrelativistic Limit of the phi^4 Theory in 2+1 Dimensions

TL;DR

This paper investigates the transition from relativistic to nonrelativistic regimes in a 2+1 dimensional phi^4 quantum field theory, deriving an effective action by analyzing scattering amplitudes and self-energy corrections.

Contribution

It provides a detailed derivation of the nonrelativistic limit and constructs an effective action for the phi^4 theory in 2+1 dimensions, including loop corrections.

Findings

Effective nonrelativistic action derived from relativistic theory

Separation of high and low energy contributions in scattering amplitude

Two-loop self-energy corrections computed

Abstract

We study the nonrelativistic limit of the quantum theory of a real scalar field with quartic self-interaction. The two body scattering amplitude is written in such way as to separate the contributions of high and low energy intermediary states. From this result and the two loop computation of the self energy correction, we determine an effective nonrelativistic action.