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The aim of the paper is to provide a constructive method for recovering a unitary matrix from experimental data. Since there is a natural immersion of unitary matrices within the set of double stochastic ones, the problem to solve is to find necessary and sufficient criteria that separate the two sets. A complete solution is provided for the 3-dimensional(More)
The aim of the paper is to make a comparison between the unitarity condition method and the standard version of the unitarity triangle approach by using as parameters four independent moduli |Uij |. This choice is motivated by the measurability property and leads to a simple criterion for the separation of unistochastic matrices from the double stochastic(More)
In this paper we provide an analytical procedure which leads to a system of (n−2)2 polynomial equations whose solutions will give the parametrization of the complex n×n Hadamard matrices. The key ingredient is a new factorization of unitary matrices in terms of n diagonal phase matrices interlaced with n−1 orthogonal matrices each one generated by a real(More)
We develop here a simple quantisation formalism that make use of Lie algebra properties of the Poisson bracket. When the brackets {H,φi} and {φi, φj}, where H is the Hamiltonian and φi are primary and secondary constraints, can be expressed as functions of H and φi themselves, the Poisson bracket defines a Poisson-Lie structure. When this algebra has a(More)
A novel method to obtain parameterizations of complex inverse orthogonal matrices is provided. These matrices are natural generalizations of complex Hadamard matrices which depend on non zero complex parameters. The method we use is via doubling the size of inverse complex conference matrices. When the free parameters take values on the unit circle the(More)
By using an exact method to impose unitarity on the neutrino data we show that around the central values of the moduli of the PMNS matrix there is a continuous approximate unitary set of matrices, all of them being consistent with a maximal CP violation in the lepton sector, i.e. δ ≈ 90◦, over a wide range for Ve3 values.
We use in this paper an exact method to impose unitarity on moduli of the neutrino PMNS matrix recently determined, and show how one could obtain information on CP non-conservation from a limited experimental information. One suggests a novel type of global fit by expressing all the theoretical quantities in terms of convention independent parameters, the(More)