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Il Nuovo Cimento A (1965-1970)

, Volume 42, Issue 3, pp 493–515 | Cite as

The discontinuity of a general feynman integral and regge poles in perturbation theory

  • B. Hamprecht
Article

Summary

A formula for the complete discontinuity across the cut of an arbitrary Feynman integral is derived. One-variable dispersion relations for a certain range of the other variable are established. Mellin transforms are extended to Feynman integrals with indefinite coefficients ofs andt in the Feynman denominator. This extension is nontrivial. Finally a method is derived that allows treatment of the leading asymptotic behaviour in terms of Legendre functions instead of only in terms of powers of the variable going to infinity. It is shown that in all cases in which a leading\(( - t)^{\alpha _i (s)} \) behaviour has been obtained for a class of Feynman integrals summed, a Regge pole can explicitely be shown to exist in the Regge plane. The pole structure in the Regge plane is shown to be simpler than the one in the α-plane.

Keywords

Regge Pole Pole Structure Landau Equation Feynman Integral Ladder Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Riassunto

Si deduce una formula per la discontinuità completa nel taglio di un integrale di Feynman arbitrario. Si scrivono le relazioni di dispersione di una variabile per un certo intervallo di valori dell'altra variabile. Si estendono le trasformazioni di Mellin agli integrali di Feynman con coefficienti indefiniti dis et nel denominatore di Feynman. Questa estensione non è banale. Infine si deduce un metodo che permette di trattare il comportamento asintotico dominante in termini delle funzioni di Legendre invece che soltanto in termini di potenze della variabile tendente all'infinito. In tutti i casi in cui si è ottenuto un comportamento dominante\(( - t)^{\alpha _i (s)} \) per una classe di integrali di Feynman sommati, si può dimostrare esplicitamente che esiste un polo di Regge nel piano di Regge. Si dimostra che la struttura del polo nel piano di Regge è più semplice di quella nel piano α.

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Footnotes

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Copyright information

© Società Italiana di Fisica 1966

Authors and Affiliations

  • B. Hamprecht
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridge

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