nLab correlator

Idea

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

Euclidean $n$-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.

Related concepts

• n-point function

• correlator as differential form on configuration space of points

• Ward identity

• entanglement

References

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

Discussion specifically of non-perturbative monopole correlators:

• Nabil Iqbal, Monopole correlations in holographically flavored liquids, Phys. Rev. D 91, 106001 (2015) (arXiv:1409.5467)

holographic principle in quantum field theory

bulk field theory	boundary field theory
dimension $n+1$	dimension $n$
field	source
wave function	correlation function
space of quantum states	conformal blocks