LEGENDRE TRANSFORMS OF SCATTERING AMPLITUDES AND A CROSSING-SYMMETRIC REPRESENTATION

Journal Article · Sun Mar 01 04:00:00 EST 1964 · Nuovo Cimento (Italy) Divided into Nuovo Cimento A and Nuovo Cimento B

DOI:https://doi.org/10.1007/BF02821673· OSTI ID:4032617

Eden, R J

Legendre transforms differ from partial-wave amplitudes by the use of variables of integration that are more appropriate for crossing symmetry. It is shown that their holomorphy properties are similar to those of partial-wave amplitudes. Using Legendre transforms the Watson-Sommerfeld transformation can be applied in a crossingsymmetric form, and the asymptotic terms can be separated from the background integral in all three energy channels simultaneously. The background integral can be expressed with an exponential factor that decreases it the contour can be moved to the left in the complex l-plane. The background integral satisfies the Mandelstam representation without subtractions, and each asymptotic term has the corresponding cut-plane analyticity with correct thresholds. (auth)

• Research Organization: CERN, Geneva
• Sponsoring Organization: USDOE
• NSA Number: NSA-18-018764
• OSTI ID: 4032617
• Journal Information: Nuovo Cimento (Italy) Divided into Nuovo Cimento A and Nuovo Cimento B, Journal Name: Nuovo Cimento (Italy) Divided into Nuovo Cimento A and Nuovo Cimento B Vol. Vol: (10), 31; ISSN NUCIA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ANALYTIC FUNCTIONS
CROSSING SYMMETRY
DIFFERENTIAL EQUATIONS
ENERGY
FIELD THEORY
INTEGRALS
MANDELSTAM REPRESENTATION
MATHEMATICS
PHYSICS
QUANTUM MECHANICS
SCATTERING
SCATTERING AMPLITUDE