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

Quantum Deformation of igl(n) Algebra on Quantum Space

We study quantum deformed $gl(n)$ and $igl(n)$ algebras on a quantum space discussing multi-parametric extension. We realize elements of deformed $gl(n)$ and $igl(n)$ algebras by a quantum fermionic space. We investigate a map between deformed $igl(2)$ algebras of our basis and other basis.Comment: 14 pages, Latex, version published in Mod. Phys. Lett.

Pion Production Model - Connection between Dynamics and Quark Models

We discuss the difficulties in testing the hadron models by using the N^* parameters extracted from the empirical amplitude analyses of the pi-N and gamma-N reaction data. As an alternative or perhaps a more advantageous approach, we present a Hamiltonian formulation that can relate the pion production dynamics and the constituent quark models of N^* structure. The application of the approach in investigating the Delta and N^*(S_{11}) excitations is reviewed. It is found that while the Delta excitation can be described satisfactory, the pi-N scattering in S_{11} channel can not be described by the constituent quark models based on either the one-gluon-exchange or one-meson-exchange mechanisms. A phenomenological quark-quark potential has been constructed to reproduce the S_{11} amplitude.Comment: 11 pages, 4 figures, to be published in Proceedings of NSTAR2000 workshop held at Jefferson Laboratory, Feb., 200

PCAC Relation and Pion Production-Absorption in Nuclei

Nuclear PCAC relation is studied in the framework of the effective theory of nuclear interaction, in which the interaction of real pion production-absorption is expressed by many-body operators, and does not include the one-nucleon operator as was assumed in the conventional works, while the effective axial-vector current includes the one-nucleon current in contrast to the former interaction. This problem is investigated under the simple linear $\sigma$-model. Results are as folows: 1) The theory describes consistently the PCAC relation and the pion production-absorption process. 2) The conventional interpretation of the effective pion source function as the interaction Hamiltonian of pion production-absorption does not hold. 3) The effective pion source function still includes the one-nucleon operator for the pion production-absorption at threshold effectively, which may justify the conventional theory.Comment: 12 pages, 3 figure

Parameter Learning of Logic Programs for Symbolic-Statistical Modeling

We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, that runs for a class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have been developed independently in each research field. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can significantly outperform the Inside-Outside algorithm