Low’s theorem
E1015932
Low’s theorem is a result in quantum electrodynamics that constrains the behavior of scattering amplitudes involving the emission of low-energy (soft) photons.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Low’s theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T13014326 — 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: Low’s theorem Context triple: [Francis E. Low, notableWork, Low’s theorem]
-
A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
B.
Erdős–Szekeres theorem
The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
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C.
Tucker’s lemma
Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
-
D.
Turán's theorem
Turán's theorem is a fundamental result in extremal graph theory that determines the maximum number of edges a graph can have without containing a complete subgraph of a given size.
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E.
Helly’s theorem
Helly’s theorem is a fundamental result in convex geometry that gives conditions under which a family of convex sets in Euclidean space has a nonempty common intersection.
- 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: Low’s theorem Target entity description: Low’s theorem is a result in quantum electrodynamics that constrains the behavior of scattering amplitudes involving the emission of low-energy (soft) photons.
-
A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
B.
Erdős–Szekeres theorem
The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
-
C.
Tucker’s lemma
Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
-
D.
Turán's theorem
Turán's theorem is a fundamental result in extremal graph theory that determines the maximum number of edges a graph can have without containing a complete subgraph of a given size.
-
E.
Helly’s theorem
Helly’s theorem is a fundamental result in convex geometry that gives conditions under which a family of convex sets in Euclidean space has a nonempty common intersection.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
result in quantum electrodynamics
ⓘ
theorem ⓘ |
| appliesTo |
both tree‑level and loop‑corrected amplitudes (for soft limit structure)
ⓘ
processes with external charged particles ⓘ scattering amplitudes ⓘ |
| assumes | photon energy much smaller than characteristic energy scale of the process ⓘ |
| characterizes |
leading terms in soft‑photon expansion of amplitudes
ⓘ
subleading terms in soft‑photon expansion of amplitudes ⓘ |
| clarifies | universal nature of soft‑photon emission in QED ⓘ |
| concerns |
low‑energy photon emission
ⓘ
soft photons ⓘ |
| describes | behavior of scattering amplitudes with soft photon emission ⓘ |
| ensures | universal factorization of soft‑photon emission ⓘ |
| field | quantum electrodynamics ⓘ |
| holdsToOrder |
leading order in soft‑photon energy
ⓘ
subleading order in soft‑photon energy ⓘ |
| implies | soft‑photon factors depend only on external charges and momenta ⓘ |
| imposes | constraints on infrared behavior of amplitudes ⓘ |
| influenced | later developments in soft‑theorem program in quantum field theory ⓘ |
| involves | expansion of amplitudes in powers of photon momentum ⓘ |
| isDerivedUsing |
Lorentz invariance
ⓘ
analytic properties of scattering amplitudes ⓘ gauge invariance ⓘ |
| isFormulatedIn | momentum space ⓘ |
| isReferencedIn |
literature on infrared problems in gauge theories
ⓘ
quantum field theory textbooks ⓘ |
| isRelatedTo |
Bloch–Nordsieck mechanism
ⓘ
Weinberg’s soft‑photon theorem ⓘ
linked to:
Low’s soft-photon theorem
infrared divergences in QED ⓘ soft‑graviton theorems (by analogy) ⓘ soft‑photon theorems ⓘ
linked to:
Low’s soft-photon theorem
|
| isValidIn | on‑shell scattering processes ⓘ |
| originalContext | radiative corrections in quantum electrodynamics ⓘ |
| relates | amplitudes with and without an additional soft photon ⓘ |
| requires |
conservation of electric charge
ⓘ
on‑shell external charged legs ⓘ |
| usedFor |
checking consistency of QED calculations involving soft photons
ⓘ
deriving universal soft‑photon factors in scattering cross sections ⓘ understanding cancellation of infrared divergences between real and virtual photons ⓘ |
| wasFormulatedBy | Francis E. Low ⓘ |
| yearProposed | 1958 ⓘ |
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: Low’s theorem Description of subject: Low’s theorem is a result in quantum electrodynamics that constrains the behavior of scattering amplitudes involving the emission of low-energy (soft) photons.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.