A model for an electrodynamics which respects gauge invariance but violates Lorentz invariance supplements the usual Maxwell Lagrangian with terms drawn from a four-vector

(a) Find the restrictions that must be imposed on d(vector)to ensure that a gauge transformation does not alter the dynamics.

(b) Assume that d(vector) is a constant four-vector. Is this consistent with your answer to part (a)? Find the Chern-Simons Maxwell equations which replace the usual Maxwell equations. Confirm that the theory is gauge invariant but does not respect Lorentz invariance.

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d = (d, ido):