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The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions. The Lagrangian for the model is
where the scalar field is complex, F μ ν = ∂ μ A ν − ∂ ν A μ {\displaystyle F_{\mu \nu }=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu }} is the electromagnetic field tensor, and D μ = ∂ μ − i A μ {\displaystyle D_{\mu }=\partial _{\mu }-\mathrm {i} A_{\mu }} the covariant derivative containing the electric charge e {\displaystyle e} of the electromagnetic field.
Assume that λ {\displaystyle \lambda } is nonnegative. Then if the mass term is tachyonic, m 2 < 0 {\displaystyle m^{2}<0} there is a spontaneous breaking of the gauge symmetry at low energies, a variant of the Higgs mechanism. On the other hand, if the squared mass is positive, m 2 > 0 {\displaystyle m^{2}>0} the vacuum expectation of the field ϕ {\displaystyle \phi } is zero. At the classical level the latter is true also if m 2 = 0 {\displaystyle m^{2}=0}. However, as was shown by Sidney Coleman and Erick Weinberg, even if the renormalized mass is zero, spontaneous symmetry breaking still happens due to the radiative corrections.
The same can happen in other gauge theories. In the broken phase the fluctuations of the scalar field ϕ {\displaystyle \phi } will manifest themselves as a naturally light Higgs boson, as a matter of fact even too light to explain the electroweak symmetry breaking in the minimal model - much lighter than vector bosons. There are non-minimal models that give a more realistic scenarios. Also the variations of this mechanism were proposed for the hypothetical spontaneously broken symmetries including supersymmetry.