Abstract:
The mass matrices of the charged leptons and neutrinos, previously derived in a minimal S_3-invariant extension of the Standard Model, were reparametrized in terms of their eigenvalues. We obtained explicit, analytical expressions for all entries in the neutrino mixing matrix, V_PMNS, the neutrino mixing angles and the Majorana phases as functions of the masses of charged leptons and neutrinos in excellent agreement with the latest experimental values. The resulting V_PMNS matrix is very close to the tri-bimaximal form of the neutrino mixing matrix. We also derived explicit analytical expressions for the matrices of the Yukawa couplings and computed the branching ratios of some selected flavour changing neutral current processes as functions of the masses of the charged leptons and the neutral Higgs bosons. We find that the S_3 x Z_2 flavour symmetry and the strong mass hierarchy of the charged leptons strongly suppress the FCNC processes in the leptonic sector well below the present experimental upper bounds by many orders of magnitude.

Abstract:
We derive closed analytical expressions for the complex Berry phase of an open quantum system in a state which is a superposition of resonant states and evolves irreversibly due to the spontaneous decay of the metastable states. The codimension of an accidental degeneracy of resonances and the geometry of the energy hypersurfaces close to a crossing of resonances differ significantly from those of bound states. We discuss some of the consequences of these differences for the geometric phase factors, such as: Instead of a diabolical point singularity there is a continuous closed line of singularities formally equivalent to a continuous distribution of `magnetic' charge on a diabolical circle; different classes of topologically inequivalent non-trivial closed paths in parameter space, the topological invariant associated to the sum of the geometric phases, dilations of the wave function due to the imaginary part of the Berry phase and others.

Abstract:
We study the complex geometric phase acquired by the resonant states of an open quantum system which evolves irreversibly in a slowly time dependent environment. In analogy with the case of bound states, the Berry phase factors of resonant states are holonomy group elements of a complex line bundle with structure group C*. In sharp contrast with bound states, accidental degeneracies of resonances produce a continuous closed line of singularities formally equivalent to a continuous distribution of "magnetic" charge on a "diabolical" circle, in consequence, we find different classes of topologically inequivalent non-trivial closed paths in parameter space.

Abstract:
Assuming that the lepton, quark and Higgs fields belong to the three-dimensional reducible representation of the permutation group S_3, we suggest a minimal S_3 invariant extension of the standard model. We find that in the leptonic sector, the exact S_3 x Z_2 symmetry, which allows 6 real independent parameters with two CP-violating phases, is consistent with experimental data and predicts a maximal mixing of the atmospheric neutrinos, and that the third neutrino is the lightest neutrino. With the exact S_3 only, there are 10 real parameters and five phases in the quark sector. A set of values of these parameters that are consistent with experimental observations is given.

Abstract:
Recent interest in flavour or horizontal symmetry building (mass textures) has been spurred mainly by the large top mass and, hence, the strong hierarchy in quark masses. Recently, various symmetry breaking schemes have been proposed based on the discrete, non-Abelian group S3L x S3R, which is broken according to S3L x S3R > S3_diag > S2_diag. The group S3 treats three objects symmetrically, while the hierarchical nature of the Yukawa matrices is a consequence of the representation structure, 1 + 2, of S3, which treats the generations differently. Different ansaetze for the breaking of the sub-nuclear democracy give different Hermitian mass matrices, M, of the same modified Fritzsch type which differ in the numerical value of the ratio M_23/M_22. A fit to the experimentally determined absolute values of the elements of the CKM matrix gives bounds on the possible values of the CP violating phase and gives a clear indication on the preferred symmetry breaking scheme. A parametrization of the CKM mixing matrix in terms of four quark mass ratios and one CP violating phase in very good agreement with the absolute value of the experimentally determined values of the CKM matrix elements is obtained.

Abstract:
A new cosmological model leads to testable predictions that are different from those of both standard cosmology and models with a cosmological constant. The prediction that q_0=0 is the same as in other ``coasting universe'' models, but arises without the need for any exotic form of matter or other ad hoc assumptions.

Abstract:
Different ansaetze for the breaking of the flavour permutational symmetry according to S(3)L X S(3)R in S(2)L X S(2) give different Hermitian mass matrices of the same modified Fritzsch type, which differ in the symmetry breaking pattern. In this work we obtain a clear and precise indication on the preferred symmetry breaking scheme from a fit of the predicted theoretical Vckm to the experimentally determined absolute values of the elements of the CKM matrix. The preferred scheme leads to simple mass textures and allows us to compute the CKM mixing matrix, the Jarlskog invariant J, and the three inner angles of the unitarity triangle in terms of four quark mass ratios and only one free parameter: the CP violating phase Phi. Excellent agreement with the experimentally determined absolute values of the entries in the CKM matrix is obtained for Phi = 90 deg. The corresponding computed values of the Jarlskog invariant and the inner angles are J = 3.00 X 10^-5, alpha= 84 deg, beta= 24 deg and gamma =72 deg in very good agreement with current data on CP violation in the neutral kaon-antikaon system and oscillations in the B-Bbar system.

Abstract:
We emphasize that there is no spin-statistics connection in nonrelativistic quantum mechanics. In several recent papers, including Phys. Rev. A 67, 042102 (2003) [quant-ph/0207017], quantum mechanics is modified so as to force a spin-statistics connection, but the resulting theory is quite different from standard physics.

Abstract:
The phase equivalence of the theoretical quark mixing matrix ${\bf V}^{th}$ derived from the breaking of the flavour permutational symmetry and the phenomenological parametrizations ${\bf V}^{PDG}$ and ${\bf V}^{KM}$ is explicitly exhibited. From here, we derive exact explicit expressions for the three mixing angles and the CP violating phase of the two phenomenological parametrizations in terms of the quark mass ratios $(m_{u}/m_{t}, m_{c}/m_{t}, m_{d}/m_{b}, m_{s}/m_{b})$ and the parameters $Z^{*1/2}$ and $\Phi^*$ characterizing the preferred symmetry breaking pattern. The computed values for the CP violating phase and the mixing angles of the standard parametrization advocated by the Particle Data Group are $\delta^*_{13}=73.2^\circ$, $\sin\theta^*_{12}=0.222$, $\sin\theta^*_{13}=0.0036$, and $\sin\theta^*_{23}=0.040$. The computed values of the CP-violating phase and the mixing angles of the Kobayashi-Maskawa parametrization are $\delta^*_{KM}=96.4^\circ$, $\sin\theta^*_{1}=0.2225$, $\sin\theta^*_{2}=0.0384$, and $\sin\theta^*_{3}=0.0162$. In both cases, the numerical values of the mixing angles and CP-violating phase computed from quark masses and the flavour symmetry breaking parameters coincide almost exactly with the central values of the same parameters obtained from a fit to experimental data.