nLab correlator



Algebraic Quantum Field Theory

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



field theory:

Lagrangian field theory


quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization



States and observables

Operator algebra

Local QFT

Perturbative QFT



In Euclidean field theory a correlator is an expectation value of observables in a given state. For the product of nn local field observables Φ(x)\mathbf{\Phi}(x) this is also called an n-point function, see there for more.

Euclidean nn-point functions are typically distributions of several variables with singularities on the fat diagonal. Their restriction of distributions to the complement of the fat diagonal hence yields a non-singular distribution exhibiting the correlator as a differential form on a configuration space of points.

Under Wick rotation (if applicable, see Osterwalder-Schrader theorem) this translates correlators to n-point functions in relativistic field theory.

In functorial quantum field theory a correlator is simply the value of the functor on a given (class of) cobordisms.


See most any text on quantum field theory/statistical mechanics.

Discussion specifically of non-perturbative monopole correlators:

holographic principle in quantum field theory

bulk field theoryboundary field theory
dimension n+1n+1dimension nn
wave functioncorrelation function
space of quantum statesconformal blocks

Last revised on May 27, 2022 at 10:52:38. See the history of this page for a list of all contributions to it.