Note on thermodynamic fermion loop under constant magnetic field

The one-loop effective potential of a thermodynamic fermion loop under constant magnetic field is studied. As expected, it can be interpreted literally as a discretized sum of $(D-2)$-dimensional energy density above the Dirac sea. Large/small mass expansions of the potential are also examined.Comment: 8 page

Quantum Group and qq-Virasoro Current in Fermion Systems

We discuss a generalization of the quantum group \su to the $q$-Virasoro algebra in two-dimensional electrons system under uniform magnetic field. It is shown that the integral representations of both algebras are reduced to those in a (1+1)-dimensional fermion. As an application of the quantum group symmetry, we discuss a model of quantum group current on the analogy of the Hall current.Comment: 20 pages, Latex. Title change

Landau Levels and Quantum Group

We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wavefunctions of the system. The quantum group symmetry commutes with the Hamiltonian and is relevant to the Landau level degeneracy. The deformation parameter $q$ of the quantum algebra turns out to be given by the fractional filling factor $\nu=1/m$ ($m$ odd integer).Comment: (revised version), 10 pages, OS-GE-36-9

Quantum Group Symmetry and Quantum Hall Wavefunctions on a Torus

We find a quantum group structure in two-dimensional motion of nonrelativistic electrons in a uniform magnetic field on a torus. The representation basis of the quantum algebra is composed of the quantum Hall wavefunctions proposed by Haldane-Rezayi at the Landau-level filling factor $\nu=1/m$ ($m$ odd). It is also shown that the quantum group symmetry is relevant to the degenerate Landau states and the deformation parameter of the quantum algebra is given by the filling factor.Comment: 9 pages, OS-GE-39-9

On thermal phase structure of deformed Gross-Neveu model

We illustrate the phase structure of a deformed two-dimensional Gross-Neveu model which is defined by undeformed field contents plus deformed Pauli matrices. This deformation is based on two motives to find a more general polymer model and to estimate how $q$-deformed field theory affects on its effective potential. There found some regions where chiral symmetry breaking and restoration take place repeatedly as temperature increasing.Comment: 13 pages plus 6 figure

SU(3) dibaryons in the Einstein-Skyrme model

SU(3) collective coordinate quantization to the regular solution of the B=2 axially symmetric Einstein-Skyrme system is performed. For the symmetry breaking term, a perturbative treatment as well as the exact diagonalization method called Yabu-Ando approach are used. The effect of the gravity on the mass spectra of the SU(3) dibaryons and the symmetry breaking term is studied in detail. In the strong gravity limit, the symmetry breaking term significantly reduces and exact SU(3) flavor symmetry is recovered.Comment: 9 pages, 14 figure

Phase Diagram of Gross-Neveu Model at Finite Temperature, Density and Constant Curvature

We discuss a phase structure of chiral symmetry breaking in the Gross-Neveu model at finite temperature, density and constant curvature. The effective potential is evaluated in the leading order of the $1/N$-expansion and in a weak curvature approximation. The third order critical line is found on the critical surface in the parameter space of temperature, chemical potential and constant curvature.Comment: 11 pages, Latex. 3 figures (eps files

Quantum affine transformation group and covariant differential calculus

We discuss quantum deformation of the affine transformation group and its Lie algebra. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators. The deformation of the group is achieved by using the adjoint representation. The elements of quantum matrix form a Hopf algebra. Furthermore, we construct a differential calculus which is covariant with respect to the action of the quantum matrix.Comment: LaTeX 22 pages OS-GE-34-94 RCNP-05