renormalization group
E575044
The renormalization group is a mathematical framework in theoretical physics that systematically studies how physical systems and their parameters change with scale, crucial for understanding critical phenomena and quantum field theories.
All labels observed (1)
| Label | Occurrences |
|---|---|
| renormalization group canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T6198499 — 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: renormalization group Context triple: [Kenneth Wilson, notableWork, renormalization group]
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A.
Lectures on Phase Transitions and the Renormalization Group
*Lectures on Phase Transitions and the Renormalization Group* is a widely used advanced physics textbook that provides a clear, modern introduction to critical phenomena, scaling, and renormalization group methods in statistical mechanics and condensed matter physics.
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B.
Pauli–Villars regularization
Pauli–Villars regularization is a technique in quantum field theory that controls ultraviolet divergences by introducing auxiliary heavy fields to render integrals finite.
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C.
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.
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D.
Slavnov–Taylor identities
Slavnov–Taylor identities are relations in non-Abelian gauge theories that generalize Ward identities, ensuring the consistency and renormalizability of gauge-invariant quantum field theories.
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E.
Yang–Lee theory
Yang–Lee theory is a framework in statistical mechanics and phase transition theory that studies the distribution of zeros of the partition function in the complex plane to understand critical phenomena.
- 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: renormalization group Target entity description: The renormalization group is a mathematical framework in theoretical physics that systematically studies how physical systems and their parameters change with scale, crucial for understanding critical phenomena and quantum field theories.
-
A.
Lectures on Phase Transitions and the Renormalization Group
*Lectures on Phase Transitions and the Renormalization Group* is a widely used advanced physics textbook that provides a clear, modern introduction to critical phenomena, scaling, and renormalization group methods in statistical mechanics and condensed matter physics.
-
B.
Pauli–Villars regularization
Pauli–Villars regularization is a technique in quantum field theory that controls ultraviolet divergences by introducing auxiliary heavy fields to render integrals finite.
-
C.
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.
-
D.
Slavnov–Taylor identities
Slavnov–Taylor identities are relations in non-Abelian gauge theories that generalize Ward identities, ensuring the consistency and renormalizability of gauge-invariant quantum field theories.
-
E.
Yang–Lee theory
Yang–Lee theory is a framework in statistical mechanics and phase transition theory that studies the distribution of zeros of the partition function in the complex plane to understand critical phenomena.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
concept in theoretical physics
ⓘ
mathematical framework ⓘ |
| appliesTo |
Heisenberg model
NERFINISHED
ⓘ
Ising model NERFINISHED ⓘ Kondo problem NERFINISHED ⓘ electroweak theory NERFINISHED ⓘ phi^4 theory ⓘ quantum chromodynamics NERFINISHED ⓘ turbulence models ⓘ |
| coreIdea |
integrate out short-distance degrees of freedom
ⓘ
rescale system to restore original form ⓘ track evolution of parameters under scale transformations ⓘ |
| developedBy |
Dmitry Shirkov
NERFINISHED
ⓘ
Kenneth Wilson NERFINISHED ⓘ Leo Kadanoff NERFINISHED ⓘ Nikolay Bogoliubov NERFINISHED ⓘ |
| explains |
asymptotic freedom in non-abelian gauge theories
ⓘ
critical exponents ⓘ decoupling of high-energy modes ⓘ running of coupling constants ⓘ scaling laws ⓘ universality near critical points ⓘ |
| field |
condensed matter physics
ⓘ
quantum field theory ⓘ statistical physics ⓘ theoretical physics ⓘ |
| introducedBy |
Francis Low
NERFINISHED
ⓘ
Murray Gell-Mann NERFINISHED ⓘ |
| relatedConcept |
Wilsonian renormalization group
NERFINISHED
ⓘ
beta function ⓘ critical surface ⓘ epsilon expansion ⓘ fixed point ⓘ functional renormalization group ⓘ momentum-shell renormalization ⓘ operator product expansion ⓘ |
| studies |
behavior of systems under changes of length scale
ⓘ
coarse graining procedures ⓘ critical phenomena ⓘ effective field theories ⓘ fixed points of scale transformations ⓘ flow of coupling constants ⓘ phase transitions ⓘ scale dependence of physical systems ⓘ universality classes ⓘ |
| usedFor |
analyzing high-energy behavior of quantum field theories
ⓘ
analyzing low-energy limits of quantum field theories ⓘ computing critical exponents ⓘ constructing effective field theories ⓘ multiscale analysis of physical systems ⓘ |
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
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: renormalization group Description of subject: The renormalization group is a mathematical framework in theoretical physics that systematically studies how physical systems and their parameters change with scale, crucial for understanding critical phenomena and quantum field theories.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.