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In field theory, the Stueckelberg action describes a massive spin-1 field as an R ] Yang–Mills theory coupled to a real scalar field φ. This scalar field takes on values in a real 1D affine representation of R with m as the coupling strength.
This is a special case of the Higgs mechanism, where, in effect, λ and thus the mass of the Higgs scalar excitation has been taken to infinity, so the Higgs has decoupled and can be ignored, resulting in a nonlinear, affine representation of the field, instead of a linear representation — in contemporary terminology, a U nonlinear σ-model.
Gauge-fixing φ=0, yields the Proca action.
This explains why, unlike the case for non-abelian vector fields, quantum electrodynamics with a massive photon is, in fact, renormalizable, even though it is not manifestly gauge invariant.