Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

The Riemann Surface of the Scattering Amplitude

Chan Hong-Mo
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 261, No. 1306 (May 16, 1961), pp. 329-356
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/2414285
Page Count: 28
  • Read Online (Free)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Riemann Surface of the Scattering Amplitude
Preview not available

Abstract

The first part of the paper bridges the gap between Khuri (1957) and Peierls (1959). The Fredholm technique is used to study the analytic properties of the scattering amplitude as a function of both the energy and the momentum transfer for Schrödinger and Klein-Gordon scattering from cut-off potentials and potentials with exponential and Yukawa tails. The discussion is extended to the case with several discrete channels. The second part deals with relativistic scattering of elementary particles. Conjectures concerning the Riemann surface of the amplitude for the elastic scattering of two identical particles and neglecting the production of further particles are formulated. With the use of the Mandelstam conjecture (1958), 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 with 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 on connexion with the Castillejo-Dalitz-Dyson ambiguity (1956).

Page Thumbnails

  • Thumbnail: Page 
329
    329
  • Thumbnail: Page 
330
    330
  • Thumbnail: Page 
331
    331
  • Thumbnail: Page 
332
    332
  • Thumbnail: Page 
333
    333
  • Thumbnail: Page 
334
    334
  • Thumbnail: Page 
335
    335
  • Thumbnail: Page 
336
    336
  • Thumbnail: Page 
337
    337
  • Thumbnail: Page 
338
    338
  • Thumbnail: Page 
339
    339
  • Thumbnail: Page 
340
    340
  • Thumbnail: Page 
341
    341
  • Thumbnail: Page 
342
    342
  • Thumbnail: Page 
343
    343
  • Thumbnail: Page 
344
    344
  • Thumbnail: Page 
345
    345
  • Thumbnail: Page 
346
    346
  • Thumbnail: Page 
347
    347
  • Thumbnail: Page 
348
    348
  • Thumbnail: Page 
349
    349
  • Thumbnail: Page 
350
    350
  • Thumbnail: Page 
351
    351
  • Thumbnail: Page 
352
    352
  • Thumbnail: Page 
353
    353
  • Thumbnail: Page 
354
    354
  • Thumbnail: Page 
355
    355
  • Thumbnail: Page 
356
    356