Coleman–Weinberg potential

The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions. The Lagrangian for the model is

${\displaystyle L=-{\frac {1}{4}}(F_{\mu \nu })^{2}+(D_{\mu }\phi )^{2}-m^{2}\phi ^{2}-{\frac {\lambda }{6}}\phi ^{4}}$

where the scalar field is complex, ${\displaystyle F_{\mu \nu }=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu }}$ is the electromagnetic field tensor, and ${\displaystyle D_{\mu }=\partial _{\mu }-\mathrm {i} (e/\hbar c)A_{\mu }}$ the covariant derivative containing the electric charge ${\displaystyle e}$ of the electromagnetic field.

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