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On the reconstruction of a unitary matrix from its moduli

1991; Springer Science+Business Media; Volume: 140; Issue: 3 Linguagem: Inglês

10.1007/bf02099133

1432-0916

G. Auberson, A. Martin, G. Mennessier,

Medical Imaging Techniques and Applications

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.