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.
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
complex-analysis technique
ⓘ
mathematical transform ⓘ method in theoretical physics ⓘ |
| advantage |
connects discrete spectrum to complex-plane singularities
GENERATED
ⓘ
facilitates study of high-energy behavior at fixed momentum transfer GENERATED ⓘ |
| appliedIn |
hadron-hadron scattering
GENERATED
ⓘ
high-energy asymptotics of scattering amplitudes GENERATED ⓘ nuclear scattering GENERATED ⓘ potential scattering GENERATED ⓘ |
| basedOn |
Cauchy residue theorem
GENERATED
ⓘ
contour integration GENERATED ⓘ |
| coreConcept |
Regge poles
GENERATED
ⓘ
analytic continuation of partial waves GENERATED ⓘ complex angular momentum GENERATED ⓘ |
| field |
Regge theory
GENERATED
ⓘ
complex analysis GENERATED ⓘ high-energy physics GENERATED ⓘ mathematical physics GENERATED ⓘ quantum field theory GENERATED ⓘ scattering theory GENERATED ⓘ |
| historicalPeriod | mid-20th century theoretical physics GENERATED ⓘ |
| namedAfter |
Arnold Sommerfeld
GENERATED
ⓘ
George N. Watson GENERATED ⓘ |
| operatesOn |
partial-wave series
GENERATED
ⓘ
sums over angular momentum quantum number l GENERATED ⓘ |
| output | contour integral in complex angular momentum plane GENERATED ⓘ |
| property |
makes Regge trajectories manifest
GENERATED
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relies on analytic structure of partial-wave amplitudes GENERATED ⓘ replaces discrete sum by integral plus residues GENERATED ⓘ |
| relatedTo |
Mellin transform
GENERATED
ⓘ
Regge theory GENERATED ⓘ dispersion relations GENERATED ⓘ partial-wave expansion GENERATED ⓘ |
| requires |
analyticity of scattering amplitude in complex l-plane
GENERATED
ⓘ
knowledge of pole structure in angular momentum GENERATED ⓘ |
| usedBy |
mathematical physicists
GENERATED
ⓘ
theoretical physicists GENERATED ⓘ |
| usedFor |
Regge pole analysis
GENERATED
ⓘ
analytic continuation in angular momentum GENERATED ⓘ converting discrete sums over angular momentum into contour integrals GENERATED ⓘ partial-wave expansion analysis GENERATED ⓘ studying analytic properties of scattering amplitudes GENERATED ⓘ transforming series over integer angular momentum into complex integrals GENERATED ⓘ |
Referenced by (1)
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