Schwinger functions

E59637

Euclidean correlation function Green’s function in Euclidean space object in quantum field theory

Schwinger functions are Euclidean-space correlation functions in quantum field theory that encode the theory’s dynamics and can be analytically continued to yield physical Minkowski-space Green’s functions.

Aliases (2)

Minkowski-space Green’s functions ×1
Schwinger functionals ×1

Statements (46)

Predicate	Object
instanceOf	Euclidean correlation function → Green’s function in Euclidean space → object in quantum field theory →
analogousTo	correlation functions in classical statistical mechanics →
associatedWith	Euclidean action → partition function of a quantum field theory →
canBeAnalyticallyContinuedTo	Wightman correlation functions → time-ordered Green’s functions →
canBeObtainedBy	Wick rotating Minkowski correlation functions →
definedAs	vacuum expectation values of products of fields in Euclidean space →
dependsOn	Euclidean time variables → spatial coordinates →
domain	n-fold Cartesian product of Euclidean space →
encode	dynamics of a quantum field theory →
field	quantum field theory →
framework	axiomatic quantum field theory → constructive quantum field theory →
historicalContext	introduced in the development of Euclidean quantum field theory →
involves	Euclidean metric → imaginary time formalism →
mathematicalNature	generalized functions → tempered distributions →
namedAfter	Julian Schwinger →
order	n-point correlation function →
relatedConcept	generating functional → propagator → two-point function →
relatedTo	Euclidean quantum field theory → Schwinger functions → surface form: "Minkowski-space Green’s functions" Osterwalder–Schrader axioms → surface form: "Osterwalder–Schrader reconstruction theorem" Euclidean quantum field theory → surface form: "Wick rotation" Wightman functions → analytic continuation → path integral formulation →
satisfies	Euclidean invariance → Osterwalder–Schrader axioms → cluster decomposition property → reflection positivity → symmetry under permutations of arguments →
spaceTimeDomain	Euclidean space →
usedFor	defining Euclidean functional integrals → lattice gauge theory calculations → non-perturbative studies of quantum field theories → reconstructing Minkowski-space quantum field theories →
usedIn	lattice QCD → Euclidean quantum field theory → surface form: "statistical field theory"

Referenced by (5)

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

Osterwalder–Schrader axioms → concerns → Schwinger functions →

Euclidean quantum field theory → hasKeyConcept → Schwinger functions →

Osterwalder–Schrader axioms → relatedTo → Schwinger functions →

Schwinger functions → relatedTo → Schwinger functions →

this entity surface form: "Minkowski-space Green’s functions"

Euclidean quantum field theory → uses → Schwinger functions →

this entity surface form: "Schwinger functionals"