This is a list of
quantum field theories
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles ...
. The first few sections are organized according to their matter content, that is, the types of fields appearing in the theory. This is just one of many ways to organize quantum field theories, but reflects the way the subject is taught pedagogically.
Scalar field theory
In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation.
The only fundamental scalar quantum field that ha ...
Theories whose matter content consists of only scalar fields
*
Klein-Gordon: free scalar field theory
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φ4 theory
*
Sine-Gordon
*
Toda field theory
Spinor field theory
Theories whose matter content consists only of spinor fields
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Dirac theory: free spinor field theory
*
Thirring model
*
Nambu–Jona-Lasinio model
*
Gross–Neveu model
The Gross–Neveu (GN) model is a quantum field theory model of Dirac fermions interacting via four-fermion interactions in 1 spatial and 1 time dimension. It was introduced in 1974 by David Gross and André Neveu as a toy model for quantum c ...
Gauge field theory
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups ...
Theories whose matter content consists only of gauge fields
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Yang–Mills theory
In mathematical physics, Yang–Mills theory is a gauge theory based on a special unitary group SU(''N''), or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using t ...
*
Proca theory
*
Chern–Simons theory
The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type developed by Edward Witten. It was discovered first by mathematical physicist Albert Schwarz. It is named after mathematicians Shiing-Shen Chern and Jam ...
Interacting theories
*Spinor and scalar
**
Yukawa model
*Scalar and gauge
**
Scalar electrodynamics
In theoretical physics, scalar electrodynamics is a theory of a U(1) gauge field coupled to a charged spin 0 scalar field that takes the place of the Dirac fermions in "ordinary" quantum electrodynamics. The scalar field is charged, and with an ap ...
**
Scalar chromodynamics
**
Yang–Mills–Higgs
*Spinor and gauge
**
Quantum electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
(QED)
***
Schwinger model (1+1D case of QED)
**
Quantum chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type ...
(QCD)
*Scalar, spinor and gauge
**
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
Sigma models
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Non-linear sigma model
In quantum field theory, a nonlinear ''σ'' model describes a scalar field which takes on values in a nonlinear manifold called the target manifold ''T''. The non-linear ''σ''-model was introduced by , who named it after a field correspondi ...
*
Wess–Zumino–Witten model
In theoretical physics and mathematics, a Wess–Zumino–Witten (WZW) model, also called a Wess–Zumino–Novikov–Witten model, is a type of two-dimensional conformal field theory named after Julius Wess, Bruno Zumino, Sergei Novikov and Ed ...
Supersymmetric quantum field theories
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Wess–Zumino model
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Supersymmetric Yang–Mills
*
Seiberg–Witten theory
In theoretical physics, Seiberg–Witten theory is a theory that determines an exact low-energy effective action (for massless degrees of freedom) of a \mathcal = 2 supersymmetric gauge theory—namely the metric of the moduli space of vacua.
...
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Super QCD
In theoretical physics, super QCD is a supersymmetric gauge theory which resembles quantum chromodynamics (QCD) but contains additional particles and interactions which render it supersymmetric.
The most commonly used version of super QCD is in 4 ...
(sQCD)
Superconformal quantum field theories
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N = 4 supersymmetric Yang–Mills theory
''N'' = 4 supersymmetric Yang–Mills (SYM) theory is a mathematical and physical model created to study particles through a simple system, similar to string theory, with conformal symmetry. It is a simplified toy theory based on Ya ...
*
ABJM superconformal field theory
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6D (2,0) superconformal field theory
String theories
Theories studied in the branch of quantum field theory known as
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
. These theories are without supersymmetry.
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Polyakov action
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Nambu-Goto action
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Bosonic string theory
Bosonic string theory is the original version of string theory, developed in the late 1960s and named after Satyendra Nath Bose. It is so called because it contains only bosons in the spectrum.
In the 1980s, supersymmetry was discovered in the co ...
Other quantum field theories
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Chiral model
In nuclear physics, the chiral model, introduced by Feza Gürsey in 1960, is a phenomenological model describing effective interactions of mesons in the chiral limit (where the masses of the quarks go to zero), but without necessarily mentioning ...
*
Kondo model (s-d model)
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Minimal model (Virasoro minimal model)
Branches of quantum field theory
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String theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
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Conformal field theory
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometime ...
*
Supersymmetry
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
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Topological quantum field theory
In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.
Although TQFTs were invented by physicists, they are also of mathe ...
*
Noncommutative quantum field theory
In mathematical physics, noncommutative quantum field theory (or quantum field theory on noncommutative spacetime) is an application of noncommutative mathematics to the spacetime of quantum field theory that is an outgrowth of noncommutative ...
*
Local quantum field theory (also known as Algebraic quantum field theory or AQFT)
{{String theory topics
Quantum field theory
Supersymmetric quantum field theory
String theory