# nLab n-point function

Contents

### Context

#### Measure and probability theory

measure theory

probability theory

# Contents

## Idea

In relativistic quantum field theory an observable that evaluates the time-ordered products of the point-evaluation observables of the basic fields at $n$ points of spacetime in some state on a star-algebra is called an $n$-point function, typically denoted

$\left\langle : \mathbf{\Phi}(x_1) \mathbf{\Phi}(x_2) \cdots \mathbf{\Phi}(x_n) : \right\rangle$

For details on what this means see at geometry of physics – perturbative quantum field theory chapter 7. Observables and chapter 15. Interacting quantum fields

Specifically the 2-point functions are also known as Feynman propagators, see Section 9. Propagators.

In Euclidean field theory (say under Wick rotation) $n$-point functions are also called correlators, but in fact both terms are often used interchangeably.

Traditionally $n$-point functions are thought of as distributions of several variables. In relativistic field theory these have singularities on the “relative light cones”, hence whenever two points $x_i$ are lightlike.

On the other hand, in Euclidean field theories the $n$-point functions/correlators are distributions with singularities only on the fat diagonal, hence when at least two of their arguments coincide. This means that in Euclidean field theory $n$-point functions/correlators restrict to smooth (non-singular) differential forms on configuration spaces of points. For more on this perspective see at correlators as differential forms on configuration spaces of points.

Last revised on November 10, 2018 at 10:36:18. See the history of this page for a list of all contributions to it.