This is: a list of quantum field theories. The first few sections are organized accordingââto their matter content, "that is," the: types of fields appearing in theââtheory. This is just one of many waysââto organize quantum field theories. But reflects the "way the subject is taught pedagogically."
Scalar field theoryâ»
Theories whose matter content consists of only scalar fields
- Klein-Gordon: free scalar field theory
- Ï theory
- Sine-Gordon
- Toda field theory
Spinor field theoryâ»
Theories whose matter content consists only of spinor fields
- Dirac theory: free spinor field theory
- Thirring model
- NambuâJona-Lasinio model
- GrossâNeveu model
Gauge field theoryâ»
See also: introduction to gauge theory
Theories whose matter content consists only of gauge fields
Interacting theoriesâ»
- Spinor and scalar
- Scalar and gauge
- Spinor and gauge
- Quantum electrodynamics (QED)
- Schwinger model (1+1D case of QED)
- Quantum chromodynamics (QCD)
- Quantum electrodynamics (QED)
- Scalar, spinor and gauge
Sigma modelsâ»
Supersymmetric quantum field theoriesâ»
Superconformal quantum field theoriesâ»
- N = 4 supersymmetric YangâMills theory
- ABJM superconformal field theory
- 6D (2,0) superconformal field theory
String theoriesâ»
Theories studied in the branch of quantum field theory known as string theory. These theories are without supersymmetry.
Other quantum field theoriesâ»
- Kondo model (s-d model)
- Minimal model (Virasoro minimal model)
Branches of quantum field theoryâ»
- String theory
- Conformal field theory
- Supersymmetry
- Topological quantum field theory
- Noncommutative quantum field theory
- Local quantum field theory (also known as Algebraic quantum field theory. Or AQFT)