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Harmonic analysis on the timelike and spacelike hyperboloids: Application to inclusive reactions

Применение к инклюзивным реакциям гармонического анализа на времени-подобных и пространственно-подобных гиперболоидах

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Il Nuovo Cimento A (1965-1970)

Summary

The timelike and spacelike hyperboloids are homogeneous spaces with respect to the Lorentz group,viz. the quotient spacesSL 2,C /SU 2 andSL 2,C /SU 1.1. The scattering amplitude possesses sufficient analyticity to continue from the timelike to the spacelike region. Starting from the harmonic analysis in theSU 1.1 basis for functions defined on the timelike sheet, with the aid of analytic continuation, we deduce the harmonic analysis for functions defined on the spacelike sheet in anSU 2 basis. The mathematical procedure is illustrated in detail by considering the three-body scattering amplitude, which is relevant for a discussion of inclusive reactions.

Riassunto

Gli iperboloidi temporali e spaziali sono spazi omogenei rispetto al gruppo di Lorentz, cioè gli spazi quozienteSL 2,C /SU 2 eSL 2,C /SU 1.1. L'ampiezza di scattering possiede sufficiente analiticità per continuare dalla regione temporale a quella spaziale. Partendo dall'analisi armonica nella base diSU 1.1 per funzioni definite sul foglietto temporale, tramite la continuazione analitica, si deduce l'analisi armonica per funzioni definite sul foglietto spaziale in una base diSU 2. Il procedimento matematico è illustrato in dettaglio considerando l'ampiezza di scattering di tre corpi, che è importante per una discussione delle reazioni inclusive.

Резюме

Времени-подобные и пространственно-подобные гиперболоиды представляют пространства, однородные относительно группы Лорентца, то есть пространства отнощенийSL 2,C /SU 2 иSL 2,C /SU 1.1. Амплитуда рассеяния является достаточно аналитической для продолжения из времени-лодобной в пространственноподобную области. Исхода из гармонического анализа наSU 1,1 базисе для функций, определенных на времени-подобном листе, мы выводим, используя аналитическое продолжение, гармонический анализ для функций, определенных на пространственноподобном листе наSU 2 базисе. Математическая процедура иллюстрируется подробно на примере трех-частичной амплитуды рассеяния, которая рассматривается в инклюзивных реакциях.

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References

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Authors and Affiliations

  1. Tata Institute of Fundamental Research, Bombay

    J. Pasupathy

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  1. J. Pasupathy
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Pasupathy, J. Harmonic analysis on the timelike and spacelike hyperboloids: Application to inclusive reactions. Nuov Cim A 17, 681–697 (1973). https://doi.org/10.1007/BF02786842

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  • DOI: https://doi.org/10.1007/BF02786842

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