The Riemann Surface of the Scattering Amplitude
The Fredholm technique is used to study analytic properties of the scattering amplitude as a function of both the energy and the momentum transfer, for Schrodinger and Klein-Gordon scattering from cut-off potentials and potentials with exponential and Yakawa tails. The discussion is extended to the case with several discrete channels. Relativistic scattering of elementary particles is discussed. Conjectures concerning the Riemann surface of the amplitude for the elastic scattering of two identical particles are formulated, neglecting the production of further particles. With the use of the Mandelstam conjecture it is found that the Riemann "surface" belonging to the scattering amplitude as an analytic function of the two independent Mandelstam variables has at least eight "sheets". The analogy between potential scattering and perturbation theory suggests the existence of further branch points on the "unphysical" sheets, which would make the structure of the full Riemann "surface" very complicated. Poles representing bound and metastable states on the Riemann surface are discussed. The reality and unitarity conditions are formulated and their implications studied.
- Research Organization:
- Univ. of Birmingham, Eng.
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-15-018967
- OSTI ID:
- 4005754
- Journal Information:
- Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences, Journal Name: Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences Journal Issue: 1306 Vol. 261; ISSN 1364-5021
- Publisher:
- The Royal Society Publishing
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
Similar Records
Analytic properties of off-energy shell potential scattering amplitudes
UNITARITY AND ANALYTICITY IN THE COMPLEX ENERGY PLANE OF GENERAL SCATTERING AMPLITUDES