Sommerfeld-Watson transform
E543033
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Sommerfeld-Watson transform canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5766809 — 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: Sommerfeld-Watson transform Context triple: [Regge theory, hasMathematicalTool, Sommerfeld-Watson transform]
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A.
Poisson summation formula
The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
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B.
Wightman functions
Wightman functions are vacuum expectation values of time-ordered products of quantum fields that rigorously encode the correlation structure and axiomatic foundations of relativistic quantum field theory.
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C.
Mittag-Leffler function
The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
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D.
Sommerfeld radiation condition
The Sommerfeld radiation condition is a mathematical criterion in wave and scattering theory that selects physically meaningful, outward-radiating solutions to the Helmholtz equation at infinity.
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E.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
- 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: Sommerfeld-Watson transform Target entity description: The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
-
A.
Poisson summation formula
The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
-
B.
Wightman functions
Wightman functions are vacuum expectation values of time-ordered products of quantum fields that rigorously encode the correlation structure and axiomatic foundations of relativistic quantum field theory.
-
C.
Mittag-Leffler function
The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
-
D.
Sommerfeld radiation condition
The Sommerfeld radiation condition is a mathematical criterion in wave and scattering theory that selects physically meaningful, outward-radiating solutions to the Helmholtz equation at infinity.
-
E.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
complex-analysis technique
ⓘ
mathematical transform ⓘ method in theoretical physics ⓘ |
| advantage |
connects discrete spectrum to complex-plane singularities
ⓘ
facilitates study of high-energy behavior at fixed momentum transfer ⓘ |
| appliedIn |
hadron-hadron scattering
ⓘ
high-energy asymptotics of scattering amplitudes ⓘ nuclear scattering ⓘ potential scattering ⓘ |
| basedOn |
Cauchy residue theorem
ⓘ
contour integration ⓘ |
| coreConcept |
Regge poles
ⓘ
linked to:
Regge theory
analytic continuation of partial waves ⓘ complex angular momentum ⓘ |
| field |
Regge theory
ⓘ
complex analysis ⓘ high-energy physics ⓘ mathematical physics ⓘ quantum field theory ⓘ scattering theory ⓘ |
| historicalPeriod | mid-20th century theoretical physics ⓘ |
| namedAfter |
Arnold Sommerfeld
ⓘ
George N. Watson ⓘ |
| operatesOn |
partial-wave series
ⓘ
sums over angular momentum quantum number l ⓘ |
| output | contour integral in complex angular momentum plane ⓘ |
| property |
makes Regge trajectories manifest
ⓘ
relies on analytic structure of partial-wave amplitudes ⓘ replaces discrete sum by integral plus residues ⓘ |
| relatedTo |
Mellin transform
ⓘ
linked to:
Mellin transforms
Regge theory ⓘ dispersion relations ⓘ partial-wave expansion ⓘ |
| requires |
analyticity of scattering amplitude in complex l-plane
ⓘ
knowledge of pole structure in angular momentum ⓘ |
| usedBy |
mathematical physicists
ⓘ
theoretical physicists ⓘ |
| usedFor |
Regge pole analysis
ⓘ
linked to:
Regge theory
analytic continuation in angular momentum ⓘ converting discrete sums over angular momentum into contour integrals ⓘ partial-wave expansion analysis ⓘ studying analytic properties of scattering amplitudes ⓘ transforming series over integer angular momentum into complex integrals ⓘ |
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: Sommerfeld-Watson transform Description of subject: The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.