Correlation Dynamics of Yukawa-theory in 1+1 dimensions

TL;DR

This paper applies correlation dynamics to analyze a Yukawa field theory in 1+1 dimensions, revealing the significant impact of 4-point functions on the system's properties through a hierarchy of Green functions.

Contribution

It introduces a correlation dynamics approach with a 4th order Green function truncation to study Yukawa theory in low dimensions.

Findings

Connected 4-point functions strongly influence system properties.

Effective potential evaluated on a torus shows notable effects from higher-order correlations.

Method demonstrates the importance of including up to 4th order Green functions.

Abstract

Using the method of correlation dynamics we investigate the properties of a field-theory for fermions and scalar bosons coupled via a Yukawa interaction. Within this approach, which consists in an expansion of full equal-time Green functions into connected equal-time Green functions and a corresponding truncation of the hierarchy of equations of motion we carry out calculations up to 4th order in the connected Green functions and evaluate the effective potential of the theory in 1+1 dimensions on a torus. Comparing the different approximations we find a strong influence of the connected 4-point functions on the properties of the system.