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  • Open Access

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

Ricardo Avila1,*, Albert Yu. Petrov2,†, Carlos M. Reyes3,‡, César Riquelme4,3,§, and Angel Sanchez5,∥

  • *Contact author: ravilav@ucsh.cl
  • †Contact author: petrov@fisica.ufpb.br
  • ‡Contact author: creyes@ubiobio.cl
  • §Contact author: ceriquelme@udec.cl
  • ∥Contact author: ansac@ciencias.unam.mx
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Phys. Rev. D 114, 055050 – Published 28 September, 2026

DOI: https://doi.org/10.1103/743q-ddwk

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 four canonical modes. One massive transverse photon, a ghost mode, a massless longitudinal mode and an additional degenerate massless mode associated with the double pole structure of the propagator. The higher-order gauge model is canonically quantized and as expected the resulting algebra of creation and annihilation operators exhibits an indefinite metric structure. 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 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.

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Phys. Rev. D 114, 055050– Published 28 September, 2026
  • Received 2 September 2025
  • Accepted 3 September 2026
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