Wick’s theorem

E59630

theorem in quantum field theory

Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.

Jump to: Surface forms Statements Referenced by

Observed surface forms (3)

Surface form	Occurrences
Wick's theorem	1
Wick’s theorem for Grassmann fields	1
Wick’s theorem for thermal (finite-temperature) field theory	1

Statements (47)

Predicate	Object
instanceOf	theorem in quantum field theory ⓘ
appliesTo	bosonic fields ⓘ creation and annihilation operators ⓘ fermionic fields ⓘ free quantum fields ⓘ scalar fields ⓘ
assumes	Gaussian (free) vacuum state ⓘ fields satisfy canonical (anti)commutation relations ⓘ
category	mathematical physics theorem ⓘ
centralConceptIn	covariant perturbation theory ⓘ many-body quantum theory ⓘ
clarifies	relation between operator products and Feynman propagators ⓘ
defines	contraction as the difference between time-ordered and normal-ordered products of two fields ⓘ
describes	expansion of time-ordered products of field operators ⓘ
field	quantum field theory ⓘ
foundationFor	Feynman diagrams ⓘ surface form: Feynman diagram technique path-integral diagrammatic expansions ⓘ
generalizedBy	Wick’s theorem self-linksurface differs ⓘ surface form: Wick’s theorem for Grassmann fields Wick’s theorem self-linksurface differs ⓘ surface form: Wick’s theorem for thermal (finite-temperature) field theory
hasKeyConcept	Green’s functions ⓘ propagators ⓘ vacuum expectation value ⓘ
historicalPeriod	mid-20th century ⓘ
holdsIn	Heisenberg operator formulation of quantum mechanics ⓘ surface form: Heisenberg picture of quantum field theory
implies	higher n-point Green’s functions of free fields factorize into products of two-point functions ⓘ time-ordered vacuum expectation values can be expressed in terms of two-point functions ⓘ
involvesOperation	contraction of two field operators ⓘ normal-ordering operator ⓘ time-ordering operator ⓘ
mathematicalForm	T(ϕ₁…ϕₙ)=:ϕ₁…ϕₙ:+(all single contractions)+…+(all full contractions) ⓘ
namedAfter	Gian-Carlo Wick ⓘ
relatedTo	Gaussian integration identities ⓘ Isserlis’ theorem in probability theory ⓘ
relatesConcept	contractions of field operators ⓘ normal-ordered products ⓘ time-ordered products ⓘ
requires	vacuum expectation values of normal-ordered products vanish ⓘ
statesThat	a time-ordered product of free fields can be written as a sum of normal-ordered products with all possible contractions ⓘ
usedFor	derivation of Feynman rules ⓘ diagrammatic expansions in quantum field theory ⓘ evaluation of S-matrix elements ⓘ normal-ordering of interaction Hamiltonians ⓘ perturbation theory in quantum field theory ⓘ systematic computation of n-point correlation functions ⓘ
usedIn	canonical operator formalism of quantum field theory ⓘ derivation of propagators ⓘ proofs of equivalence between operator and path-integral formalisms ⓘ

Referenced by (4)

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

Wick’s theorem → generalizedBy → Wick’s theorem self-linksurface differs ⓘ

this entity surface form: Wick’s theorem for thermal (finite-temperature) field theory

Wick’s theorem → generalizedBy → Wick’s theorem self-linksurface differs ⓘ

this entity surface form: Wick’s theorem for Grassmann fields

Dyson series → relatedTo → Wick’s theorem ⓘ

this entity surface form: Wick's theorem

Feynman rules → relatedTo → Wick’s theorem ⓘ