Gell-Mann–Low theorem

E59631

theorem in quantum field theory

The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.

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All labels observed (2)

Label	Occurrences
Gell-Mann–Low theorem canonical	2
Gell-Mann–Low renormalization group equation	1

Statements (47)

Predicate	Object
instanceOf	theorem in quantum field theory ⓘ
appliesTo	Heisenberg operator formulation of quantum mechanics ⓘ surface form: Heisenberg picture fields interaction picture fields ⓘ
assumes	existence of adiabatic limit ⓘ stability of the vacuum under adiabatic switching ⓘ unique interacting vacuum state ⓘ
category	theorem in mathematical physics ⓘ
clarifies	relation between bare and interacting fields ⓘ role of interaction picture in QFT ⓘ
concerns	time evolution with switched-on interaction Hamiltonian ⓘ vacuum expectation values of time-ordered products ⓘ
connects	time-ordered correlation functions of interacting fields to free-field ones ⓘ
context	renormalized perturbation theory ⓘ
field	quantum field theory ⓘ
formalism	operator formalism of quantum field theory ⓘ
hasConsequence	expression of interacting Green’s functions via functional derivatives of generating functional ⓘ justification of perturbative expansion around free theory ⓘ
historicalContext	developed in early years of renormalized quantum field theory ⓘ
implies	Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED ⓘ surface form: Dyson series expansion for the S-matrix
importance	fundamental result for the foundations of perturbative QFT ⓘ
involves	S-matrix ⓘ time-ordered exponentials ⓘ vacuum-to-vacuum transition amplitudes ⓘ
mathematicalFormulation	expresses interacting vacuum as limit of time-evolution operator acting on free vacuum ⓘ
namedAfter	Francis E. Low ⓘ Murray Gell-Mann ⓘ
provides	rigorous connection between interacting and free fields ⓘ
relatedTo	Dyson’s formula ⓘ LSZ reduction formula ⓘ interaction picture time-evolution operator ⓘ renormalization theory ⓘ
relates	free (bare) vacuum state ⓘ free quantum fields ⓘ interacting quantum fields ⓘ interacting vacuum state ⓘ
requires	adiabatic factor e^{-\epsilon \|t\|} in interaction Hamiltonian ⓘ
underpins	Dyson series ⓘ perturbation theory in quantum field theory ⓘ
usedBy	quantum field theorists ⓘ
usedFor	calculation of correlation functions ⓘ construction of perturbative expansions ⓘ definition of Green’s functions ⓘ derivation of Feynman rules ⓘ
usedIn	perturbative calculations in particle physics ⓘ relativistic quantum field theory ⓘ scattering theory ⓘ
usesConcept	adiabatic switching of interactions ⓘ

Referenced by (3)

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

Dyson series → relatedTo → Gell-Mann–Low theorem ⓘ

Francis E. Low → notableWork → Gell-Mann–Low theorem ⓘ

Francis E. Low → knownFor → Gell-Mann–Low theorem ⓘ

this entity surface form: Gell-Mann–Low renormalization group equation