Summary
A method to continue analytically Roy’s equations to any energy is investigated. The supplementary conditions to perform such a continuation are Mandelstam representation with a finite number of subtractions and some other rather weak conditions on the double-spectral functions. The fact that the continuation has to be performed after quite tedious calculations and the difficulties with the estimation of errors are the main disadvantages of the method. On the other hand, it provides a complete test of analyticity, crossing and unitarity for a partial-wave set without any limitations in energy.
Riassunto
Si studia un metodo per la continuazione analitica delle equazioni di Roy fino a qualsiasi energia. Le condizioni supplementari necessarie per effettuare tale continuazione sono costituite dalla rappresentazione di Mandelstam con un numero finito di sottrazioni e da alcune altre condizioni deboli per funzioni spettrali doppie. I principali inconvenienti del metodo sono rappresentati dal fatto che la continuazione si può effettuare solo dopo calcoli abbastanza complicati e dal fatto che esistono difficoltà nel calcolo degli errori. D’altra parte, tale metodo mette a disposizione una prova completa di analiticità, di incrocio e di unitarietà per un insieme di onde parziali, senza limitazioni nell’energia.
Реэюме
Исследуется метод аналитического продолжения уравнений Роя на случай проиэвольных знергий. Дополнительные условия для осушествления такого продолжения составляют представление Манделстама с конечным числом вычитаний и некоторые другие довольно слабые условия на двойные спектральные функции. Тот факт, что аналитическое продолжение должно быть проведено после довольно трудоемких вычислений, и трудности с оценкой ощибок представляют основные недостатки зтого метода. С другой стороны зтот метод обеспечивает полную проверку аналитичности, кроссинг-симметрии и унитарности для парциальной системы беэ каких-либо ограничений по знергии.
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References
S. M. Roy:Phys. Lett.,36 B, 353 (1971).
J. L. Basdevant, J. C. Le Guillou andH. Navelet:Nuovo Cimento,7 A, 363 (1972);M. R. Pennington andS. D. Protopopescu: preprint LBL-963 (1972);J. L. Basdevant, C. D. Froggatt andJ. L. Petersen:Phys. Lett.,41 B, 173, 178 (1972).
Y. S. Jin andA. Martin:Phys. Rev.,135, B 1375 (1964).
A. Martin:Nuovo Cimento,42, 933 (1966);44, 1219 (1966).
C. López andF. J. Ynduráin:Padé Approximants and Their Applications, edited byP. R. Graves-Morris (New York, 1973), p. 217.
R. Courant andD. Hilbert:Methods of Mathematical Physics, Vol.1 (New York, 1953).
F. W. Byron andR. W. Fuller:Mathematics of Classical and Quantum Physics, Vol.1 and2 (Reading, Mass., 1969).
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López, C. Extension of Roy’s exact partial-wave equations to any energy. Nuov Cim A 18, 794–804 (1973). https://doi.org/10.1007/BF02727594
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DOI: https://doi.org/10.1007/BF02727594