Correlation function (quantum field theory): Difference between revisions

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{{short description|Expectation value of time-ordered quantum operators}}

In [[quantum field theory]], '''correlation functions''', often referred to as '''correlators''' or '''[[Green's function (many-body theory)|Green's functions]]''', are [[vacuum expectation value|vacuum expectation values]] of [[time ordering|time-ordered]] products of field operators. They are a key object of study in quantum field theory where they can be used to calculate various [[observable|observables]] such as [[S-matrix]] elements, although they are not themselves observables. This is because they need not be [[gauge theory|gauge invariant]], nor are they [[uniqueness quantification|unique]], with different correlation functions resulting in the same S-matrix and therefore describing the same [[physics]].<ref>{{cite arxivarXiv|last1=Manohar|first1=A.V.|authorlink1=|date=2018|title=Introduction to Effective Field Theories|pages=|arxiveprint=1804.05863}}</ref> They are closely related to [[correlation function]]s between [[random variable]]s, although they are nonetheless different objects, being defined in [[Minkowski space]]time and on quantum operators.

== Definition ==