Drinfeld twists and algebraic Bethe ansatz of the supersymmetric t-J model
We construct the Drinfeld twists (factorizing F-matrices) for the supersymmetric t-J model. Working in the basis provided by the F-matrix (i.e. the so-called F-basis), we obtain completely symmetric representations of the monodromy matrix and the pseudo-particle creation operators of the model. These enable us to resolve the hierarchy of the nested Bethe vectors for the gl(2|1) invariant t-J model.

title: Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
abstract: The anisotropic spin-1/2 chains with arbitrary boundary fields are diagonalized with the off-diagonal Bethe ansatz method. Based on the properties of the R-matrix and the K-matrices, an operator product identity of the transfer matrix is constructed at some special points of the spectral parameter. Combining with the asymptotic behavior (for XXZ case) or the quasi-periodicity properties (for XYZ case) of the transfer matrix, the extended T-Q ansatzes and the corresponding Bethe ansatz equations are derived.

title: Primary fields and screening currents of gl(2|2) non-unitary conformal field theory
abstract: The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields.

title: Eigenvalues of Ruijsenaars–Schneider models associated with An−1 root system in Bethe ansatz formalism
abstract: Ruijsenaars–Schneider models associated with An−1 root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are given in terms of the Bethe ansatz formulas. Taking the “nonrelativistic” limit, we obtain the spectrum of the corresponding Calogero–Moser systems in the third formulas of Felder et al.

title: Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
abstract: A bstractThe Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the offdiagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix and the K-matrices, certain operator product identities of the transfer matrix are obtained at some special points of the spectral parameter. These identities and the asymptotic behaviors of the transfer matrix together allow us to construct the inhomogeneous T − Q relation and the associated Bethe ansatz equations. In the diagonal boundary limit, the reduced results coincide exactly with those obtained via other methods.

title: Drinfeld twists and symmetric Bethe vectors of supersymmetric fermion models
abstract: We construct the Drinfeld twists (factorizing F-matrices) of the gl(m|n)-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the F-matrix (the F-basis). We resolve the hierarchy of the nested Bethe vectors in the F-basis for the gl(m|n) supersymmetric model.

title: Fermion Masses and Flavor Mixings from Family Symmetry SU(3)
abstract: We suggest a new particle model based on the symmetry group $SU(3)_{C}\otimes SU(2)_{L}\otimes SU(2)_{L'}\otimes SU(2)_{R}\otimes U(1)_{B-L}\otimes SU(3)_{F}\otimes U(1)_{N}$. The family symmetry and the high-energy left-handed and right-handed isospin subgroups are respectively broken by some flavon and Higgs fields one after another. At the low-energy scale the super-heavy fermions are all integrated out, the model finally leads to an effective theory with the standard model symmetry group. After the electroweak breaking all the fermion mass matrices are elegantly characterized only by six parameters. The model can perfectly fit and explain all the current experimental data about the fermion masses and flavor mixings, in particular, it finely predicts the first generation quark masses and the values of $\theta^{l}_{13}, \langle m_{\beta\beta}\rangle, J_{CP}^{l}$ in neutrino physics. The results are all promising to be tested in future experiments.

title: The frequency separations of stellar p-modes
abstract: The purpose of this work is to investigate the characteristics of a new frequency separation of stellar p-modes.  Frequency separations are deduced from the asymptotic formula of stellar p-modes. Then, using the theoretical adiabatic frequencies of stellar model, we compute the frequency separations.  A new separation sigma(l-1l+ 1)( n), which is similar to the scaled small separation d(ll+ 2)( n)/(2l + 3), is obtained from the asymptotic formula of stellar p-modes. The separations sigma(l-1l+ 1)( n) and d(ll+ 2)( n)/(2l+ 3) have the same order. And like the small separation, sigma(l)-(1l+ 1)( n) is mainly sensitive to the conditions in the stellar core. However, with the decrease in the central hydrogen abundance of stars, the separations sigma(02) and rho(13) deviate more and more from the scaled small separation. This characteristic could be used to extract the information on the central hydrogen abundance of stars.

title: Model of four generation fermions and cold dark matter and matter-antimatter asymmetry
abstract: I suggest a practical particle model as an extension to the standard model. The model has a TeV scale $U(1)_{B-L}$ symmetry and it contains the fourth generation fermions with the TeV scale masses, in which including a cold dark matter neutrino. The model can completely account for the fermion flavor puzzles, the cold dark matter, and the matter-antimatter asymmetry through the leptogenesis. In particular, it is quite feasible and promising to test the model in future experiments.

title: Associated production of a Higgs boson with tau sleptons in the CP violating MSSM at future e^+ e^- colliders
abstract: We investigate the production of the lightest neutral Higgs boson in association with tau sleptons in the CP violating minimal supersymmetric standard model (MSSM) at future high-energy $e^{+}e^{-}$ linear colliders. In parameter space of the constrained MSSM, the production cross section of $e^{+}e^{-}\to h^0\widetilde{\tau}^+_1\widetilde{\tau}^-_1$ can be very substantial at high energies. This process would provide a new production mechanism of neutral Higgs bosons and open a window to probe the Higgs-stau coupling and some soft supersymmetric breaking parameters at next linear colliders.

title: Grand Canonical Ensembles in General Relativity
abstract: We develop a formalism for general relativistic, grand canonical ensembles in space-times with timelike Killing fields. Using that, we derive ideal gas laws, and show how they depend on the geometry of the particular space-times. A systematic method for calculating Newtonian limits is given for a class of these space-times, which is illustrated for Kerr space-time. In addition, we prove uniqueness of the infinite volume Gibbs measure, and absence of phase transitions for a class of interaction potentials in anti-de Sitter space.