Abelian gauge field equations

Abstract

Abstract This chapter studies the Abelian gauge field theory. It starts with a discussion of covariance, contravariance, and invariance, which provide the necessary foundations to develop relativistic field theory. Next, it introduces the Klein-Gordon equation and then it explores what the symmetry of the underlying theory offers. In particular, we see that gauge field and electromagnetism arise as a natural consequence of the need to preserve local internal symmetry. It then considers various notions of symmetry breaking, especially spontaneous symmetry breaking. It shows in such a context that gauge field again plays an important role through the celebrated Higgs mechanism