Correlation function (quantum field theory)

Quantum field theory
Feynman diagram
History
Background Field theory Electromagnetism Weak force Strong force Quantum mechanics Special relativity General relativity Gauge theory
Symmetries Symmetry in quantum mechanics C-symmetry P-symmetry T-symmetry Space translation symmetry Time translation symmetry Rotation symmetry Lorentz symmetry Poincaré symmetry Gauge symmetry Explicit symmetry breaking Spontaneous symmetry breaking Yang–Mills theory Noether charge Topological charge
Tools Anomaly Crossing Effective field theory Expectation value Ghost fields Faddeev–Popov ghosts Feynman diagram Lattice gauge theory LSZ reduction formula Partition function Propagator Quantization Regularization Renormalization Vacuum state Wick's theorem Wightman axioms
Equations Dirac equation Klein–Gordon equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations
Standard Model Quantum electrodynamics Electroweak interaction Quantum chromodynamics Higgs mechanism
Incomplete theories Topological quantum field theory String theory Superstring theory M-Theory Supersymmetry Supergravity Technicolor Theory of everything Quantum gravity
Scientists C. D. Anderson P. W. Anderson Bethe Bjorken Bogoliubov Brout Callan Coleman DeWitt Dirac Dyson Englert Fermi Feynman Fierz Fock Fröhlich Glashow Gell-Mann Gross Guralnik Heisenberg Higgs Haag Hagen 't Hooft Jordan Kendall Kibble Lamb Landau Lee Majorana Mills Nambu Nishijima Parisi Polyakov Salam Schwinger Skyrme Sudarshan Tomonaga Veltman Ward Weinberg Weisskopf Weyl Wilczek Wilson Yang Yukawa

In quantum field theory, the (real space) n-point correlation function is defined as the functional average (functional expectation value) of a product of field operators at different positions

For time-dependent correlation functions, the time-ordering operator is included.

Correlation functions are also called simply correlators. Sometimes, the phrase Green's function is used not only for two-point functions, but for any correlators.

The correlation function can be interpreted physically as the amplitude for propagation of a particle or excitation between y and x. In the free theory, it is simply the Feynman propagator (for n=2).^[1]

See also

• Connected correlation function
• One particle irreducible correlation function
• Green's function (many-body theory)
• Partition function (mathematics)

References

Further reading

• Alexander Altland, Ben Simons (2006). Condensed Matter Field Theory. Cambridge University Press.
• Schroeder, Daniel V. and Michael Peskin, An Introduction to Quantum Field Theory. Addison-Wesley.