Summary
Discontinuities of the four-to-four particle amplitude across the cuts in the physical region associated with two quadrilateral singularities (Fig. 1 and 2) are evaluated byS-matrix methods. The Cutkosky formula and positive-α criterion for these singularities are deduced.
Riassunto
Con i metodi della matriceS si valutano le discontinuità dell’ampiezza delle particelle quattro per quattro attraverso i tagli nella regione fisica associata con due singolarità quadrilatere (Fig. 1 e 2). Si deducono la formula di Cutkosky e il ćriterio dell’α positivo per queste singolarità.
Similar content being viewed by others
References
For an early paper ofS-matrix theory seeW. Heisenberg:Zeits. Phys.,120, 513, 673 (1943). The various modern approaches to the subject rely heavily on analyticity properties. See for example:G. F. Chew andM. Jacob:Strong-Interaction Physics (New York, 1964);J. Gunson:Journ. Mod. Phys.,6, 827 (1964).H. P. Stapp:Phys. Rev.,125, 2139 (1962);D. I. Olive:Phys. Rev.,135, B 745 (1964). A very readable introduction isR. J. Eden, P. V. Landshoff, D. I. Olive andJ. C. Polkinghorne:The Analytic S-Matrix (Cambridge, 1966).
P. V. Landshoff andD. I. Olive:Journ. Math. Phys. (in press).
L. D. Landau:Nucl. Phys.,13, 181 (1959).
J. C. Polkinghorne:Nuovo Cimento,23, 360 (1962);25, 901 (1962).
Lectures byR. J. Eden andJ. C. Polkinghorne: Brandeis Summer Institute 1961 (New York).
S. Coleman andR. E. Norton:Nuovo Cimento,38, 438 (1965).
Papers may be traced throughP. V. Landshoff, D. I. Olive andJ. C. Polkinghorne:The hierarchical principle in perturbation theory, inNuovo Cimento (to be published).
T. Regge andG. Barucchi:Nuovo Cimento,34, 106 (1964).
Author information
Authors and Affiliations
Additional information
The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research, OAR, under Grant AF EOAR 63–79 with the European Office of Aerospace Research, United States Air Force.
Traduzione a cura della Redazione.
Rights and permissions
About this article
Cite this article
Bloxham, M.J.W. On certain physical-region singularities inS-matrix theory. Nuovo Cimento A (1965-1970) 44, 794–808 (1966). https://doi.org/10.1007/BF02911205
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02911205