Classical solutions for the Carroll-Field-Jackiw-Proca electrodynamics

Understand

In the present work, we investigate classical solutions of the Maxwell-Carroll-Field-Jackiw-Proca (MCFJP) electrodynamics for the cases a purely timelike and spacelike Lorentz-violating (LV) background.

• Starting from the MCFJP Lagrangian and the associated wave equations written for the potential four-vector, the tensor form of the Green function is achieved.
• In the timelike case, the components of the stationary Green function are explicitly written.
• The classical solutions for the electric and magnetic field strengths are then evaluated, being observed that the electric sector is not modified by the LV background, keeping the Maxwell-Proca behavior.