REGGE POLES AS CONSEQUENCES OF ANALYTICITY AND UNITARITY

Journal Article · Fri Feb 01 04:00:00 EST 1963 · Annals of Physics (New York) (U.S.)

DOI:https://doi.org/10.1016/0003-4916(63)90110-6· OSTI ID:4705131

Mandelstam, S

It is shown that a scatiering amplitude that satisfies a double- dispersion relation and elastic unitarity is meromorphic in the complex l-plane for Re l greater than some negative quantity, and that its asymptotic behavior in the momentum transfer is therefore given by the Regge formula. In the proof it is necessary to assume that the scattering amplitude is bounded by ts/sup -1/ (for pion-pion kinematics) as both s and t become infinite, but it is argued that, if this limit is not satisfied, the dispersion integrals in s will be dominated by the high-energy region and, in all probability, those in t will require an infinite number of subtractions. In contrast to the Schrodinger or BetheSalpeter cases, the positions of the Regge pole at high energy will depend on the strength of the coupling. This high-energy Regge pole appears to come into the right half-plane for repulsive potentials and to correspond to a ghost rather than bound state. If and only if it were to reach the value l = 1, the boundedness condition would no longer be satisfied. (auth)

• Research Organization: Univ. of Birmingham, Eng.
• NSA Number: NSA-17-024281
• OSTI ID: 4705131
• Journal Information: Annals of Physics (New York) (U.S.), Journal Name: Annals of Physics (New York) (U.S.) Vol. Vol: 21; ISSN APNYA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BETHE-SALPETER EQUATION
BINDING ENERGY
CROSS SECTIONS
DISPERSION THEORY
ELEMENTARY PARTICLES
ENERGY
ENERGY LEVELS
FIELD THEORY
INTERACTIONS
MATHEMATICS
MOMENTUM
PHYSICS
PIONS
QUANTUM MECHANICS
REACTION KINETICS
REGGE POLES
RELATIVITY THEORY
SCATTERING
SCHROEDINGER EQUATION