Gell-Mann–Low theorem
E59631
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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Gell-Mann–Low theorem canonical | 2 |
| Gell-Mann–Low renormalization group equation | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T478373 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Gell-Mann–Low theorem Context triple: [Dyson series, relatedTo, Gell-Mann–Low theorem]
-
A.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
B.
Gell-Mann–Nishijima formula
The Gell-Mann–Nishijima formula is a key relation in particle physics that connects a particle’s electric charge to its isospin and hypercharge, helping classify hadrons within the quark model.
-
C.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
-
D.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
-
E.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Gell-Mann–Low theorem Target entity description: 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.
-
A.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
B.
Gell-Mann–Nishijima formula
The Gell-Mann–Nishijima formula is a key relation in particle physics that connects a particle’s electric charge to its isospin and hypercharge, helping classify hadrons within the quark model.
-
C.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
-
D.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
-
E.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
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Input
Subject: Gell-Mann–Low theorem Description of subject: 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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Gell-Mann–Low renormalization group equation