Action principle and quantization of gauge fields

Abstract

It is shown that the action principle solves the quantization problem of gauge fields without the recourse to path integrals, without the use of canonical commutation rules, and without the need of going to the complicated structure of the Hamiltonian. We obtain the expression for the vacuum-to-vacuum transition amplitude directly from the action principle in the celebrated Coulomb gauge, and then finally we write the amplitude in terms of \ensuremath{\delta} functionals. To study gauge transformations, we use a variation of the Faddeev-Popov technique which is quite suitable to deal with the nonlinear transformation character involved with non-Abelian gauge fields.