Communications in Mathematical Physics

, Volume 140, Issue 3, pp 523–542 | Cite as

On the reconstruction of a unitary matrix from its moduli

  • G. Auberson
  • A. Martin
  • G. Mennessier
Article

Abstract

We study the problem of reconstructing a unitary matrix from the knowledge of the moduli of its matrix elements, first in the case of a symmetric matrix, which could be theS matrix forn coupled channels, second in the case of a non-symmetric matrix like the Cabibbo-Kobayashi-Maskawa matrix forn generations of quarks and leptons. In the symmetric case we find conditions under which the problem has\(2^{(n^2 - 3n)/2} \) solutions differing in a non-trivial way, but also situations where one has continuous ambiguities.

In the non-symmetric case we show that forn>3 there may be continuous ambiguities, of which we give an exhaustic list forn=4. We give indications that there is also a set of moduli for which one has\(2^{(n^2 - 3n)/2} \) discrete solutions, but no rigorous proof.

Keywords

Neural Network Statistical Physic Matrix Element Complex System Nonlinear Dynamics 

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • G. Auberson
    • 1
  • A. Martin
    • 2
  • G. Mennessier
    • 1
  1. 1.Laboratoire de Physique MathématiqueUSTLMontpellier Cedex 05France
  2. 2.Theory DivisionCERNGeneva 23Switzerland

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