Correlation function (quantum field theory)
Encyclopedia
In quantum field theory
, the matrix element computed by inserting a product of operators
between two states, usually the vacuum state
s, is called a correlation function
.
Sometimes, the time-ordering operator
is included. Time ordering appears in the path integral formulation
and the Schwinger-Dyson equation
s.
Without time ordering, they are called Wightman functions/Wightman distributions.
Depending on
(the number of inserted operators), the correlation functions are called one-point function (tadpole
), two-point function, and so on.
Correlation functions are also called simply correlators. Sometimes, the phrase Green's function
is used not only for two-point functions, but for any correlators.
See also connected correlation function, one particle irreducible correlation function, Green's function (many-body theory)
.
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, the matrix element computed by inserting a product of operators
Operator (physics)
In physics, an operator is a function acting on the space of physical states. As a resultof its application on a physical state, another physical state is obtained, very often along withsome extra relevant information....
between two states, usually the vacuum state
Vacuum state
In quantum field theory, the vacuum state is the quantum state with the lowest possible energy. Generally, it contains no physical particles...
s, is called a correlation function
Correlation function
A correlation function is the correlation between random variables at two different points in space or time, usually as a function of the spatial or temporal distance between the points...
.
Sometimes, the time-ordering operator
is included. Time ordering appears in the path integral formulationPath integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
and the Schwinger-Dyson equation
Schwinger-Dyson equation
The Schwinger–Dyson equation , also Dyson-Schwinger equations, named after Julian Schwinger and Freeman Dyson, are general relations between Green functions in quantum field theories...
s.
Without time ordering, they are called Wightman functions/Wightman distributions.
Depending on
(the number of inserted operators), the correlation functions are called one-point function (tadpoleTadpole (physics)
In quantum field theory, a tadpole is a one-loop Feynman diagram with one external leg, giving a contribution to a one-point correlation function . One-loop diagrams with a propagator that connects back to its originating vertex are often also referred as tadpoles...
), two-point function, and so on.
Correlation functions are also called simply correlators. Sometimes, the phrase Green's function
Green's function
In mathematics, a Green's function is a type of function used to solve inhomogeneous differential equations subject to specific initial conditions or boundary conditions...
is used not only for two-point functions, but for any correlators.
See also connected correlation function, one particle irreducible correlation function, Green's function (many-body theory)
Green's function (many-body theory)
In many-body theory, the term Green's function is sometimes used interchangeably with correlation function, but refers specifically to correlators of field operators or creation and annihilation operators....
.