Coleman–Weinberg potential

The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions. The Lagrangian for the model is L = − 1 4 ( F μ ν ) 2 + | D μ ϕ | 2 − m 2 | ϕ | 2 − λ 6 | ϕ | 4 {\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, 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 ( e / ℏ c ) A μ {\displaystyle D_{\mu }=\partial _{\mu }-\mathrm {i} (e/\hbar c)A_{\mu }} the covariant derivative containing the electric charge e {\displaystyle e} of the electromagnetic field.

Source: Wikipedia — Coleman–Weinberg potential (CC BY-SA 4.0)

Coleman–Weinberg potential

The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions. The Lagrangian for the model is L = − 1 4 ( F μ ν ) 2 + | D μ ϕ | 2 − m 2 | ϕ | 2 − λ 6 | ϕ | 4 {\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, 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 ( e / ℏ c ) A μ {\displaystyle D_{\mu }=\partial _{\mu }-\mathrm {i} (e/\hbar c)A_{\mu }} the covariant derivative containing the electric charge e {\displaystyle e} of the electromagnetic field.

Source: Wikipedia "Coleman–Weinberg potential" · CC BY-SA 4.0

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