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Il Nuovo Cimento A (1965-1970)

, Volume 41, Issue 3, pp 470–486 | Cite as

Stochastic description of extended hadrons

  • Z. Haba
  • J. Lukierski
Article

Summary

The dynamics of extended hadrons is described as a stochastic process in the imaginary proper-time variable. Internal dynamics is represented by the kernel which characterizes the probability flow of pointlike constituents. It appears that global and internal dynamics in proper time are separable, and for linearly extended hadron we derive the covariant Veneziano propagator. The invariance in dual models of Koba-Nielsen variables with respect to projective transformation is interpreted as the well-known projective invariance of the underlying Brownian motion. The generalization of the Feynman-Kac formula to the case of quantum fields describing extended objects is briefly discussed.

Стохастическое описание протяженных адронов

Реэюме

Описывается динамика протяженных адронов, как стохастический процесс по переменной мнимого собственного времени. Внутренняя динамика представляется с помошью ядра, которое характериэует вероятностный ток точечно-подобных составных частей. Окаэывается, что обшая и внутренняя динамики раэделяются по собственному времени. Для линейно протяженного адрона мы выводим ковариантный пропагатор Венециано. Инвариантность в дуальных моделях переменных Коба-Нильсена по отнощению к проективным преобраэованиям интерпретируется как хорощо иэвестная проективная инвариантность броуновского движения. Вкратце обсуждается формула Фейнмана-Кача на случай квантованных полей, описываюших протяженные общекты.

Riassunto

Si deserive la dinamica di adroni estesi come un processo stocastico nella variabile immaginaria del tempo proprio. La dinamica interna è rappresentata dal nocciolo che caratterizza il flusso di probabilità di costituenti puntiformi. Si vede che le dinamiche interna e globale sono separabili nel tempo proprio, e si deduce il propagatore covariante di Veneziano per adroni estesi linearmente. Si interpreta l’invarianza delle variabili di Koba-Nielsen in modelli duali come la ben nota invarianza proiettiva del moto Browniano di base. Si discute brevemente la generalizzazione della formula di Feynman-Kac al caso di campi quantici che descrivono oggetti estesi.

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Copyright information

© Società Italiana di Fisica 1977

Authors and Affiliations

  • Z. Haba
    • 1
  • J. Lukierski
    • 2
  1. 1.Institute of Theoretical PhysicsUniversity of WroclawWroclawPoland
  2. 2.Z.I.F., Universität BielefeldBielefeldW. Germany

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