**algebraic quantum field theory** (perturbative, on curved spacetimes, homotopical)

**quantum mechanical system**, **quantum probability**

**interacting field quantization**

A *Lagrangian field theory* is *interacting* if it is not a *free field theory*. Just as in the discussion at *free field theory*, there is some room for making this precise, but at the very least it should mean that the Euler-Lagrange equations of motion are *not linear*.

In perturbative quantum field theory the algebras of observables of interacting field theories are quantized as formal power series in Planck's constant and in the coupling constant (interacting field algebra), as a formal expansion around the quantizaton of a free field theory (Wick algebra).

To date perturbative quantum field theory is the only way known to approach the quantization of interacting field theories in spacetime dimension $\geq 4$. In constructive field theory examples of non-perturbative interacting quantum field theores in dimension 3 have been constructed and examples in dimension 2 are common, such as 2d CFTs.

Key examples of interacting field theories are phi^n theory (scalar field theory with interaction term given by the power $(\mathbf{\Phi}(x))$ of the field observable), quantum electrodynamics (with its electron-photon interaction), pure Yang-Mills theory for nonabelian gauge group, quantum chromodynamics, and gravity.

The quantization of Yang-Mills theory, as a non-perturbative quantum field theory is a famous open problem. Yang-Mills theory with abelian gauge group the circle group is a free field theory, but coupled to a Dirac field there is a canonical interaction term that makes this the interacting field theory called *quantum electrodynamics* (QED). Similarly quantum chromodynamics (QCD) is an interacting field theories. These interacting theories (QED, QCD with Higgs field-coupling) make up the standard model of particle physics.

Last revised on August 2, 2018 at 03:28:40. See the history of this page for a list of all contributions to it.