Landau pole
E334541
The Landau pole is a theoretical energy scale in quantum field theory at which a coupling constant, such as the electric charge in quantum electrodynamics, would diverge, signaling a breakdown of the theory’s validity.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Landau pole canonical | 1 |
| Landau singularity | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3175504 — 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: Landau pole Context triple: [Lev Landau, knownFor, Landau pole]
-
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.
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.
Nambu–Jona-Lasinio model
The Nambu–Jona-Lasinio model is a theoretical framework in quantum field theory that illustrates spontaneous chiral symmetry breaking and mass generation for fermions, analogous to mechanisms in superconductivity.
-
D.
Schwinger model
The Schwinger model is a two-dimensional quantum electrodynamics theory that serves as a exactly solvable toy model for studying phenomena like confinement, chiral symmetry breaking, and anomalies in quantum field theory.
-
E.
Planck scale
The Planck scale is the realm of extremely high energies and tiny distances where quantum effects of gravity are expected to dominate and classical concepts of space-time break down.
- 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: Landau pole Target entity description: The Landau pole is a theoretical energy scale in quantum field theory at which a coupling constant, such as the electric charge in quantum electrodynamics, would diverge, signaling a breakdown of the theory’s validity.
-
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.
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.
Nambu–Jona-Lasinio model
The Nambu–Jona-Lasinio model is a theoretical framework in quantum field theory that illustrates spontaneous chiral symmetry breaking and mass generation for fermions, analogous to mechanisms in superconductivity.
-
D.
Schwinger model
The Schwinger model is a two-dimensional quantum electrodynamics theory that serves as a exactly solvable toy model for studying phenomena like confinement, chiral symmetry breaking, and anomalies in quantum field theory.
-
E.
Planck scale
The Planck scale is the realm of extremely high energies and tiny distances where quantum effects of gravity are expected to dominate and classical concepts of space-time break down.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
energy scale
ⓘ
phenomenon in quantum field theory ⓘ theoretical concept ⓘ |
| appearsIn | solution of renormalization group equations ⓘ |
| arisesFrom |
logarithmic running of couplings
ⓘ
perturbative renormalization group analysis ⓘ |
| associatedWith |
positive beta function
ⓘ
renormalization group ⓘ running coupling constant ⓘ |
| characterizedBy | divergent effective coupling at finite energy scale ⓘ |
| consequence |
effective field theory description breaks down
ⓘ
need for new physics before the pole is reached ⓘ |
| contrastedWith |
asymptotic freedom
ⓘ
asymptotic safety ⓘ |
| dependsOn | beta function of the theory ⓘ |
| describes | divergence of a coupling constant ⓘ |
| domain |
high-energy physics
ⓘ
theoretical physics ⓘ |
| energyScale | very high energy ⓘ |
| field | quantum field theory ⓘ |
| hasAlternativeName |
Landau pole
ⓘ
surface form:
Landau singularity
|
| hasInterpretation | indicator of non-perturbative or new degrees of freedom ⓘ |
| implies |
need for ultraviolet completion of the theory
ⓘ
triviality problem ⓘ upper bound on validity range of a theory ⓘ |
| mathematicalFormulation | pole in the running coupling as a function of energy scale ⓘ |
| namedAfter | Lev Landau ⓘ |
| occursIn |
non-asymptotically-free gauge theories
ⓘ
quantum electrodynamics ⓘ scalar field theories ⓘ |
| relatedConcept |
cutoff scale
ⓘ
effective field theory ⓘ ultraviolet completion ⓘ |
| relatedTo |
triviality of quantum electrodynamics
ⓘ
triviality of scalar φ^4 theory ⓘ |
| relevantFor |
Standard Model Higgs sector triviality bounds
ⓘ
quantum electrodynamics ⓘ |
| requires | renormalization procedure for definition of running couplings ⓘ |
| signals |
breakdown of a quantum field theory
ⓘ
loss of predictivity of a theory ⓘ |
| theoreticalStatus | not experimentally accessible in QED ⓘ |
| usedIn | arguments for incompleteness of certain quantum field theories ⓘ |
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: Landau pole Description of subject: The Landau pole is a theoretical energy scale in quantum field theory at which a coupling constant, such as the electric charge in quantum electrodynamics, would diverge, signaling a breakdown of the theory’s validity.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Landau singularity