nLab
correlator

Contents

Context

Algebraic Quantum Field Theory

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

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

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.

holographic principle in quantum field theory

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