Bogoliubov–Parasyuk theorem
E461418
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
All labels observed (4)
| Label | Occurrences |
|---|---|
| BPHZ renormalization | 1 |
| BPHZ renormalization scheme | 1 |
| Bogoliubov–Parasyuk theorem canonical | 1 |
| Bogoliubov–Parasyuk–Hepp–Zimmermann theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4681196 — 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: Bogoliubov–Parasyuk theorem Context triple: [Nikolay Bogolyubov, notableWork, Bogoliubov–Parasyuk theorem]
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A.
Gell-Mann–Low theorem
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.
-
B.
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.
-
C.
Wick’s theorem
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.
-
D.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
-
E.
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.
- 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: Bogoliubov–Parasyuk theorem Target entity description: The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
A.
Gell-Mann–Low theorem
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.
-
B.
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.
-
C.
Wick’s theorem
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.
-
D.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
-
E.
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.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
result in quantum field theory
ⓘ
theorem ⓘ |
| addresses |
overlapping divergences
ⓘ
subdivergences in Feynman graphs ⓘ |
| aimsTo | make perturbative renormalization mathematically rigorous ⓘ |
| appliesTo |
divergent Feynman diagrams
ⓘ
perturbative quantum field theory ⓘ |
| assumes |
local quantum field theory
ⓘ
power-counting renormalizability ⓘ |
| basisFor |
BPHZ renormalization scheme
ⓘ
linked to:
Bogoliubov–Parasyuk theorem
|
| clarifies |
role of counterterms in renormalization
ⓘ
structure of divergences in Feynman graphs ⓘ |
| concerns |
Feynman integrals
ⓘ
Green functions ⓘ renormalized perturbation series ⓘ |
| countryOfOrigin | Soviet Union ⓘ |
| ensures |
consistency of renormalization procedure
ⓘ
finiteness of renormalized Green functions ⓘ |
| field | quantum field theory ⓘ |
| formulatedBy |
Nikolay Bogoliubov
ⓘ
linked to:
Nikolay Bogolyubov
Oleg Parasyuk ⓘ |
| guarantees |
locality of counterterms
ⓘ
renormalizability order by order in perturbation theory ⓘ |
| historicalContext |
development of quantum electrodynamics
ⓘ
postwar quantum field theory ⓘ |
| influenced |
axiomatic approaches to quantum field theory
ⓘ
modern renormalization theory ⓘ |
| language | originally published in Russian ⓘ |
| mathematicalDiscipline |
functional analysis
ⓘ
mathematical physics ⓘ |
| provides |
recursive subtraction scheme for divergences
ⓘ
systematic renormalization procedure ⓘ |
| relatedConcept |
counterterm method
ⓘ
normalization conditions ⓘ renormalization constants ⓘ subtraction schemes in momentum space ⓘ |
| relatedTo |
BPHZ renormalization
ⓘ
linked to:
Bogoliubov–Parasyuk theorem
Bogoliubov–Parasyuk–Hepp–Zimmermann theorem ⓘ
linked to:
Bogoliubov–Parasyuk theorem
Hepp–Zimmermann forest formula ⓘ |
| subject |
Feynman diagrams
ⓘ
renormalization ⓘ ultraviolet divergences ⓘ |
| timePeriod | mid 20th century ⓘ |
| typeOf | rigorous renormalization theorem ⓘ |
| uses | R-operation ⓘ |
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: Bogoliubov–Parasyuk theorem Description of subject: The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Bogoliubov–Parasyuk theorem
linked to: Bogoliubov–Parasyuk theorem
linked to: Bogoliubov–Parasyuk theorem