  We revisit the problem of deriving local gauge invariance with spontaneous
symmetry breaking in the context of an effective field theory. Previous
derivations were based on the condition of tree-order unitarity. However, the
modern point of view considers the Standard Model as the leading order
approximation to an effective field theory. As tree-order unitarity is in any
case violated by higher-order terms in an effective field theory, it is
instructive to investigate a formalism which can be also applied to analyze
higher-order interactions. In the current work we consider an effective field
theory of massive vector bosons interacting with a massive scalar field. We
impose the conditions of generating the right number of constraints for systems
with spin-one particles and perturbative renormalizability as well as the
separation of scales at one-loop order. We find that the above conditions
impose severe restrictions on the coupling constants of the interaction terms.
Except for the strengths of the self-interactions of the scalar field, that can
not be determined at this order from the analysis of three- and four-point
functions, we recover the gauge-invariant Lagrangian with spontaneous symmetry
breaking taken in the unitary gauge as the leading order approximation to an
effective field theory. We also outline the additional work that is required to
finish this program.
