Lorentz invariance together with gauge invariance provide strong constraints on possible generalizations of classical electrodynamics. We show here how to construct the lowest-order corrections to the Maxwell Lagrangian, and examine the implications in a few interesting cases. While the above invariance principles are not sufficient to completely determine the model, specific predictions may be obtained if we allow the remaining arbitrary parameters to take on the values obtained within a given fundamental theory-QED in the context of the present paper. This straightforward approach provides the student with a new perspective on classical electromagnetism, and on the role played by the vacuum. (C) 1996 American Association of Physics Teachers. [References: 19]
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