Lorentz- and CPT-violating models of electrodynamics with Chern-Simons terms are typically plagued by various sorts of instabilities. However, when the Chern-Simons term arises from a slow time variation in a pseudoscalar field with an axionlike electromagnetic coupling, the total energy of the theory is bounded below. We examine the behavior of such a theory, finding that in a systematic power series expansion of the magnetic and pseudoscalar fields, singularities appear in the field profiles. Some of the questionable behavior can be cured by taking a fully nonperturbative approach, but other problematic terms remain. This may be an indication that Cerenkov-like radiation will automatically carry away energy from a moving charge, preventing a charge from moving with uniform velocity over extended distances.
Digital Object Identifier (DOI)
Physical Review D, Volume 102, Issue 3, 2020, pages 035009-.
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Karki, S., & Altschul, B. (2020). Problems with Lorentz violation originating from a cosmologically varying pseudoscalar field. Physical Review D, 102(3). https://doi.org/10.1103/physrevd.102.035009