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Unitarity and the evaluation of discontinuities


If we call the connected part of theT-matrix element for the processba,, then we prove the following result. If is the boundary value of an analytic function of complex invariants, then is an opposite boundary value. This follows directly from field theory, is independent of any special invariance principles, or of crossing symmetry and is not restricted to any type of process. This result achieves validity in a much wider context than was previously believed, and emerges as a fundamental consequence of theTCP theorem. It means that unitarity provides a direct evaluation of the corresponding discontinuity.


Se ohiamiamo la parte connessa dell’elemento di matriceT per il processob→ a, allora possiamo dimostrare il seguente risultato. Se è il valore al contorno di una funzione analitica di invarianti complessi, allora è il valore al oontorno contrapposto. Questo discende direttamente dalla teoria dei campi, è indipendente da ogni speciale principio di invarianza o di simmetria incrociata e non e limitato a nessun tipo di processo. Questo risultato ha valore in un contesto piu ampio di quanto precedentemente si credesse, ed emerge come una conseguenza fondamentale del teoremaTCP. Ciò significa che l’unitarietà fornisce una valutazione diretta della corrispondente discontinuità.

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Olive, D.I. Unitarity and the evaluation of discontinuities. Nuovo Cim 26, 73–102 (1962).

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