Phi-nth quantum scalar field theories where n is not integer

[spaghetti3451]

Consider a quantum scalar field theory with interaction terms of the form $\phi^{n}$, where $n$ is not an integer.

Where are some examples of physical theories which involve such interaction terms?

 

[eljose79]

One example of a physical theory that involves such interaction terms is the Higgs field in the Standard Model of particle physics. The Higgs field has an interaction term of the form $\phi^{4}$, where $\phi$ is the Higgs field. This interaction term is crucial for giving mass to elementary particles in the Standard Model.

Another example is the theory of Bose-Einstein condensates, which describes the behavior of a collection of bosonic particles at low temperatures. The interaction between these particles is described by an effective potential that includes terms of the form $\phi^{n}$, where $\phi$ is the field that describes the condensed particles.

In condensed matter physics, the Landau theory of phase transitions also involves interaction terms of the form $\phi^{4}$ or higher powers of the field $\phi$, where $\phi$ represents the order parameter that characterizes the transition.

Finally, in cosmology, the inflationary model of the early universe involves an inflaton field with an interaction term of the form $\phi^{4}$, which plays a crucial role in driving the rapid expansion of the universe during the inflationary epoch.