Composite Operator Effective Potential Approach to QED$_3$

TL;DR

This paper compares the composite operator effective potential method with the Dyson-Schwinger approach in (2+1)-dimensional QED, showing they produce equivalent gap equations when using a specific fermion propagator ansatz.

Contribution

It demonstrates that the composite operator effective potential reproduces the same gap equations as the Dyson-Schwinger method in QED3.

Findings

Effective potential reproduces Dyson-Schwinger gap equations

Method provides an alternative calculational approach

Validates the composite operator approach in lower-dimensional QED

Abstract

The composite operator effective potential is compared with the conventional Dyson-Schwinger method as a calculational tool for (2+1)-dimensional quantum electrodynamics. It is found that when the fermion propagator ansatz is put directly into the effective potential, it reproduces exactly the usual gap equations derived in the Dyson-Schwinger approach.