Eliminating on the Divergences of the Photon Self - Energy Diagram in (2+1) Dimensional Quantum Electrodynamics

TL;DR

This paper investigates the divergences in the photon self-energy diagram in (2+1)D QED using Pauli-Villars and dimensional regularization, emphasizing the importance of gauge invariance for consistent results.

Contribution

It demonstrates that consistent divergence elimination in (2+1)D QED requires careful consideration of gauge invariance across different regularization methods.

Findings

Both regularization methods yield consistent results when gauge invariance is maintained.

Proper handling of gauge invariance is crucial for divergence elimination in (2+1)D QED.

The study clarifies the role of gauge invariance in regularization procedures.

Abstract

The divergence of the photon self - energy diagram in spinor quantum electrodynamics in $(2+1)$ dimensional space time- $(QED_3)$ is studied by the Pauli - Villars regularization and dimensional regularization. Results obtained by two different methods are coincided if the gauge invariant of theory is considered carefully step by step in these calculations.