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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

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.

Related concepts

• Feynman amplitude