BRS symmetry for Abelian gauge theories

The renormalization of Abelian gauge theories is studied by using the BRS symmetry. Comparison is made between the original BRS transformation and that supplemented by the auxiliary field B(x). It is shown that in the modified treatment of the BRS symmetry the photon remains massless after renormalization is performed without any additional constraint. We also show that the same technique allows us to renormalize the scalar electrodynamics even with the bilinear gauge condition F(A) = αdelta sub(μ)A sup(μ) + γA sub(μ)sup(2), a simple treatment of which was not possible in the conventional method. Contrary to the wide belief, our investigation shows that the BRS symmetry gives rise to all the physics contents which the gauge symmetry implied in renormalizing the Abelian theory. (author)