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 )](a/../upload/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 )](a/../upload/math/57962d2875d530cdd6aa811ccb19e579.png)
for a complex field φ.
See the analytization trick.
See phi to the fourth.
QED
See the analytization trick
See QED
Schwinger model
See Schwinger model
The Yukawa model
See Yukawa model
Yang-Mills theory
![\mathcal{L}=-\frac{1}{4g^2}Tr[F_{\mu\nu}F^{\mu\nu}]](a/../upload/math/3c53566bf1abbc9e7311fe63f49d810f.png)
See Yang-Mills, Quantum Yang-Mills theory
The Yang-Mills-Higgs model
See Yang-Mills-Higgs model
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]](a/../upload/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.
See nonlinear sigma model
Chiral model
See chiral model
The Thirring model
See Thirring model
The Sine-Gordon model
See Sine-Gordon
The Chern-Simons model
See Chern-Simons model , topological quantum field theory
The Gross-Neveu model
See Gross-Neveu
