Modern Physics Letters A

We consider heavy nonrelativistic bosons with masses M~M_GUT which arise in the Universe during phase transitions with spontaneous symmetry breaking at the grand unification scale. In the frame of statistical mechanics approach with model-independent description of cosmological background we show that the process of emerging of massive GUT bosons looks like evaporation of a Bose condensate. First massive nonrelativistic bosons behave like ideal quantum degenerate Bose gas which has the Gibbons-Hawking temperature due to the presence of the de Sitter event horizon.

We describe a geometric picture for the pattern of fermion masses of the three generations which is invariant with respect to the renormalization group below the electroweak scale. Moreover, we predict the upper limit for the ratio between the Dirac masses of the μ and τ neutrinos,

The representation, à la Schwinger, of quantum algebra SU(3)_pq is considered by constructing quantum commutation relations for p, q-deformed harmonic oscillators. The obtained results can be seen as a two-parameter extension of the quantum algebra SU(3)_q studied in Ref. 1.

Using a classical action associated to a point particle in (1+1) dimensions the classical string theory is derived. In connection with this result two aspects are clarified: First, the point particle in (1+1) dimensions is not an ordinary relativistic system, but rather some kind of relativistic top; and second, through the quantization of such kind of top, the ordinary string theory is not obtained, but rather a σ-model associated to a noncompact group which may be understood as an extended string theory.

We construct an extension of the recently proposed dynamical model for the breaking of SU(5)_GUT gauge symmetry, in which a pair of massless chiral supermultiplets for Higgs doublets are naturally obtained. We point out that a model at a specific point in the parameter space of superpotential is regarded as a low-energy effective theory of an supersymmetric gauge model for the strongly interacting hypercolor sector.

The conditions that yield deviations from a purely exponential behavior of a quantum mechanical system at short times are analyzed with special emphasis on the boundedness of the Hamiltonian. A few practical examples are considered. The problem of dissipation in quantum mechanics and quantum field theory is also briefly discussed.

An algebraic construction which is more general and closely connected with that of Faddeev,¹ along with its application for generating different classes of quantum integrable models is summarized to complement the recent results of Ref. 1.

We study the stability of a scalar inflaton field and analyze its point attractors in the phase space. We show that the value of the inflaton field in the vacuum is a bifurcation parameter and prove the possible existence of a limit cycle by using analytical and numerical arguments.

The one-loop radiative corrections to the Higgs boson potential in the MSSM, originating from the top quark and squark loops, are summed in the leading log approximation using the renormalization group (RG). The RG improved effective potential is minimized and the corrections to the CP-odd and CP-even Higgs boson masses are calculated. The resulting masses exhibit smoother top mass dependence than those calculated without RG summation. We have also found that for preferable values of the top mass the light Higgs mass does not exceed 100 GeV.