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Correlation function (quantum field theory)

 

 
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Correlation function (quantum field theory)
 
 
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In quantum field theory
Quantum field theory

Quantum field theory or QFT provides a theoretical framework for constructing quantum mechanics models of systems classically described by field or of Many-body problem....
, correlation functions generalize the concept of correlation function
Correlation function

Correlation functions contain information about the distribution of points or events, or things across some space/time.A very simple example of a correlation function is the following: Given the existence of a point at a position X in some space, what is the probability of there being another point at a second position Y....
s in statistics. In the quantum mechanical
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
 context they are computed as the matrix element of 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 with...
 inserted between two vectors, 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. The term "zero-point field" is sometimes used as a synonym for the vacuum state of an individual quantized field....
s.

Sometimes, the time-ordering operator is included. Time ordering appears in the path integral formulation
Path integral formulation

The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action of classical mechanics. It replaces the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinity of possible trajectories to compute a probability amplitude....
 and the Schwinger-Dyson equation
Schwinger-Dyson equation

The Schwinger-Dyson equation, named after Julian Schwinger and Freeman Dyson, is an equation of quantum field theory . Given a polynomially bounded functional F over the field configurations, then, for any state vector , |?>, we have...
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
Tadpole (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 ....
), two-point function, and so on.






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In quantum field theory
Quantum field theory

Quantum field theory or QFT provides a theoretical framework for constructing quantum mechanics models of systems classically described by field or of Many-body problem....
, correlation functions generalize the concept of correlation function
Correlation function

Correlation functions contain information about the distribution of points or events, or things across some space/time.A very simple example of a correlation function is the following: Given the existence of a point at a position X in some space, what is the probability of there being another point at a second position Y....
s in statistics. In the quantum mechanical
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
 context they are computed as the matrix element of 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 with...
 inserted between two vectors, 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. The term "zero-point field" is sometimes used as a synonym for the vacuum state of an individual quantized field....
s.

Sometimes, the time-ordering operator is included. Time ordering appears in the path integral formulation
Path integral formulation

The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action of classical mechanics. It replaces the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinity of possible trajectories to compute a probability amplitude....
 and the Schwinger-Dyson equation
Schwinger-Dyson equation

The Schwinger-Dyson equation, named after Julian Schwinger and Freeman Dyson, is an equation of quantum field theory . Given a polynomially bounded functional F over the field configurations, then, for any state vector , |?>, we have...
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
Tadpole (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 ....
), two-point function, and so on. The correlation functions are often 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 ordinary differential equation differential equations subject to 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....
.