Il Nuovo Cimento (1955-1965)

, Volume 9, Issue 4, pp 569–585 | Cite as

Phenomenological theory of theS-matrix andT, C andP invariance

  • J. Werle
Article

Summary

General expressions for the transition matrix are given for reactions between four particles of arbitrary spins. Restrictions imposed byT, C orP invariance requirements are expressed in terms of simple equations between some phenomenological scalar coefficients which occur in the general expression for the transition matrix. For any given type of reaction one can find in this way definite physical relations which have the advantage of being free of any special assumptions and approximations.

Riassunto

Si danno espressioni generali per la matrice di transizione delle reazioni fra quattro particelle di spin arbitrari. Le restrizioni imposte dall’esigenza dell’invarianza diT, C oP si esprimono in termini di semplici equazioni tra alcuni coefficienti scalari fenomenologici che compaiono nell’espressione generale della matrice di transizione. Per ogni dato tipo di reazione si possono così trovare relazioni fisiche definite che offrono il vantaggio di essere esenti da qualsiasi ipotesi e approssimazione generali.

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References

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    T. D. Lee andC. N. Yang:Phys. Rev.,104, 254 (1956);C. S. Wu et al.: Phys. Rev.,105, 1413 (1957);106, 1361 (1957);L. Garvin, L. M. Lederman andM. Weinrich:Phys. Rev.,105, 1415 (1957);J. Friedman andV. L. Telegdi:Phys. Rev.,105, 1681 (1957); and others. See alsoReports on the VII-th Rochester Conference andReports on the Padua-Venice Conference (1957).ADSCrossRefGoogle Scholar
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    This definition of time reversal is just a simple extension of that usede.g. byG. Lüders (Ann. of Phys.,2, 1 (1957)) and others.S. Watanabe (Rev. Mod. Phys.,27, 40 (1957)) uses another definition of time reversal which differs fromT by the operation of complex conjugation.ADSCrossRefMATHGoogle Scholar
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    The assumptions about the commutation relations used in this paper are sufficient but not necessary for the validity of theTCP theorem.E.g. we can assume that kinematically different Fermion fields commute with each other and with all Boson fields and theTCP theorem will remain valid with slightly changed definitions of the constant phase factorsϱ L. It is to be noted that in the case when the commutator (or anticommutator) of two field operators is ac-number different from zero the matrixM must be symmetrized (or antisymmetrized) in the corresponding field operators. Compare:G. Lüders:Vertauschungsrelationen zwischen verschiedenen Feldern (to be published).Google Scholar
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    Some more detailed considerations about the form of basic independent tensorsG Krsuv are given in another paper:J. Werle:Bull. Pol. Ac. Sc. (to be published).Google Scholar

Copyright information

© Società Italiana di Fisica 1958

Authors and Affiliations

  • J. Werle
    • 1
  1. 1.Institute for Nuclear Research and University of WarsawPorland

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