correlator

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

**quantum mechanical system**, **quantum probability**

**interacting field quantization**

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.

**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 |

Last revised on November 10, 2018 at 09:03:59. See the history of this page for a list of all contributions to it.