# Higher-order Chern-Simons extensions to QED in $2+1$ dimensions

## TL;DR

This paper explores a higher-order extension of QED in 2+1 dimensions with Chern-Simons terms, analyzing its quantization, radiative corrections, and causality, revealing a consistent, finite, and microcausality-preserving model with ghost states.

## Contribution

It introduces and quantizes a higher-order Chern-Simons extended QED in 2+1 dimensions, analyzing radiative corrections and demonstrating finiteness and causality preservation.

## Key findings

- Photon and ghost modes identified with a massive photon.
- Radiative corrections produce two fermionic degrees of freedom, including a ghost.
- Photon polarization and vertex corrections are finite and well-defined.

## Abstract

In this work, we investigate radiative corrections in the higher-order extension of the Maxwell-Chern-Simons model coupled to standard spinor matter in $2+1$ dimensions. We begin analyzing the higher-order gauge sector, where we find the modes and the polarizations vectors associated to a massive photon and ghost field. The higher-order gauge model is canonically quantized and as expected the resulting algebra of creation and annihilation operators corresponds to an indefinite metric in Hilbert space. Subsequently, we compute all relevant one-loop diagrams in the modified QED starting with the fermion self-energy. We show that the induced corrections to the fermion two-point function produce two independent fermionic degrees of freedom, which can be included in a redefined Lagrangian describing two decoupled fermions fields, one corresponding to a physical particle and the other to a negative-norm ghost state. We take advantage of this decomposition to compute the photon polarization operator and the vertex correction, both of which are found to be finite. Finally, we analyze the causal behavior of the model by computing the commutator of gauge fields at different spacetime points, and found that microcausality is preserved.