Examples of quantum field theory models
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φ4
![S[\phi]=\int d^dx \left (\frac{1}{2} \partial^\mu \phi(x) \partial_\mu \phi(x) -\frac{1}{2}m^2\phi(x)^2 -\frac{\lambda}{4!}\phi(x)^4\right )](/w/images/math/0f573d886957989942378cae491a6ae8.png)
for a real field φ
![S[\phi^*,\phi]=\int d^dx \left (\partial^\mu \phi^*(x) \partial_\mu \phi(x) -m^2\phi^*(x)\phi(x) -\frac{\lambda}{4}(\phi^*(x)\phi(x))^2\right )](/w/images/math/57962d2875d530cdd6aa811ccb19e579.png)
for a complex field φ.
See analytization trick.
See phi to the fourth.
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QED
See analytization trick.
See QED.
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Schwinger model
See Schwinger model.
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The Yukawa model
See Yukawa model.
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Yang-Mills theory
![\mathcal{L}=-\frac{1}{4g^2}Tr[F_{\mu\nu}F^{\mu\nu}]](/w/images/math/3c53566bf1abbc9e7311fe63f49d810f.png)
See Yang-Mills, Quantum Yang-Mills theory.
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The Yang-Mills-Higgs model
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Nonlinear sigma models
![S[\phi]=\int d^dx \left[\frac{1}{2}G_{ij}(\phi(x))\partial^\mu \phi^i(x) \partial_\mu \phi^j(x) - V(\phi(x))\right]](/w/images/math/446ef3da21e12d538038b9c9e008a2c4.png)
for some positive definite tensor G acting bilinearly upon the tangent space of the target manifold and a potential V bounded from below.
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Chiral model
See chiral model.
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The Thirring model
See Thirring model.
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The Sine-Gordon model
See Sine-Gordon.
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The Chern-Simons model
See Chern-Simons model, topological quantum field theory.
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The Gross-Neveu model
See Gross-Neveu.
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Nambu-Jona-Lasinio model
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