56,989 research outputs found

### 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 $q$-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

- …