Schwinger–Dyson equations

E130660

equations of motion integral equations system of equations

The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.

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All labels observed (3)

Label	Occurrences
Dyson–Schwinger equations	2
Schwinger–Dyson equations canonical	2
Dyson equation	1

Statements (48)

Predicate	Object
instanceOf	equations of motion ⓘ integral equations ⓘ system of equations ⓘ
alsoKnownAs	Schwinger–Dyson equations ⓘ surface form: Dyson–Schwinger equations
appliesTo	gauge theories ⓘ interacting quantum field theories ⓘ non-perturbative quantum field theory ⓘ quantum chromodynamics ⓘ quantum electrodynamics ⓘ
assumes	existence of a well-defined path integral measure ⓘ
canBeWrittenAs	hierarchy of coupled integral equations ⓘ
centralConceptIn	continuum functional methods ⓘ non-perturbative quantum field theory ⓘ
derivedFrom	functional integral identity ⓘ invariance of the path integral under field shifts ⓘ path integral formalism ⓘ
encodes	full dynamics of a quantum field ⓘ
expressedInTermsOf	effective action ⓘ generating functional of connected Green's functions ⓘ
field	quantum field theory ⓘ
forms	infinite tower of equations ⓘ
generalizes	Heisenberg operator formulation of quantum mechanics ⓘ surface form: Heisenberg equations of motion classical Euler–Lagrange equations ⓘ
historicalDevelopment	formulated in mid-20th century ⓘ
mathematicalType	functional differential equations ⓘ nonlinear integral equations ⓘ
namedAfter	Freeman Dyson ⓘ Julian Schwinger ⓘ
relatedTo	Bethe–Salpeter equation ⓘ Slavnov–Taylor identities ⓘ Ward–Takahashi identities ⓘ
relates	Green's functions ⓘ n-point correlation functions ⓘ propagators ⓘ vertex functions ⓘ
requires	renormalization for ultraviolet divergences ⓘ truncation schemes for practical calculations ⓘ
usedFor	calculation of hadron properties ⓘ dynamical chiral symmetry breaking ⓘ non-perturbative studies of confinement ⓘ resummation of Feynman diagrams ⓘ study of fermion mass generation ⓘ study of gluon and ghost propagators ⓘ study of running coupling in QCD ⓘ
usedIn	continuum QCD approaches ⓘ lattice gauge theory analyses ⓘ
validIn	Euclidean space formulation ⓘ Minkowski space-time ⓘ surface form: Minkowski space formulation

Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Julian Schwinger → notableFor → Schwinger–Dyson equations ⓘ

Julian Schwinger → notableConcept → Schwinger–Dyson equations ⓘ

Bethe–Salpeter equation → relatedTo → Schwinger–Dyson equations ⓘ

this entity surface form: Dyson–Schwinger equations

Schwinger–Dyson equations → alsoKnownAs → Schwinger–Dyson equations ⓘ

this entity surface form: Dyson–Schwinger equations

Lippmann–Schwinger equation → relatedTo → Schwinger–Dyson equations ⓘ

this entity surface form: Dyson equation