The lorentz transformations in the new quantum electrodynamics

Abstract

In the paper “Quantization of the New Field Equations—I,” written by Born and Infeld, we tried to give in the last section a proof of the invariance of the commutation rules under Lorentz transformations. The proof given there is not only very intricate, but also, as Feenberg kindly pointed out, not correct in the use of the δ-functions. As a formalism analogous to ours was recently used by H. Euler and may, perhaps, find application in the further development of the theory, it seems desirable to give a simple and strict proof of the Lorentz invariance. This is the problem with which we shall deal in this paper.