Phenomenological Study of Excited Baryons

We study baryon excited states for quark confinement and chiral symmetry breaking. In the first part we discuss spatially deformed baryon excitations. As signals of deformation, we study masses and electromagnetic transitions. Such a study of spatial structure is expected to provide information on quark binding mechanism and hence quark confinement. In the second part, we consider the chiral symmetry for baryons and study positive and negative parity baryons. We show that there are two distinctive representations of chiral symmetry for baryons. We investigate their phenomenological consequences in terms of linear sigma models.Comment: 9 pages, 2 eps figures "Talk given at the workshop Future Directions in Quark Nuclear Physics", Adelaide, March (1998

On boundaries of parabolic subgroups of Coxeter groups

In this paper, we investigate boundaries of parabolic subgroups of Coxeter groups. Let $(W,S)$ be a Coxeter system and let $T$ be a subset of $S$ such that the parabolic subgroup $W_T$ is infinite. Then we show that if a certain set is quasi-dense in $W$, then $W \partial\Sigma(W_T,T)$ is dense in the boundary $\partial\Sigma(W,S)$ of the Coxeter system $(W,S)$, where $\partial\Sigma(W_T,T)$ is the boundary of $(W_T,T)$.Comment: the full version of the paper "Addendum to `Dense subsets of the boundary of a Coxeter system'

A class of reflection rigid Coxeter systems

In this paper, we give a class of reflection rigid Coxeter systems. Let $(W,S)$ be a Coxeter system. Suppose that (1) for each $s,t\in S$ such that $m(s,t)$ is odd, $\{s,t\}$ is a maximal spherical subset of $S$, (2) there does not exist a three-points subset $\{s,t,u\}\subset S$ such that $m(s,t)$ and $m(t,u)$ are odd, and (3) for each $s,t\in S$ such that $m(s,t)$ is odd, the number of maximal spherical subsets of $S$ intersecting with $\{s,t\}$ is at most two, where $m(s,t)$ is the order of $st$ in the Coxeter group $W$. Then we show that the Coxeter system $(W,S)$ is reflection rigid. This is an extension of a result of N.Brady, J.P.McCammond, B.M\"uhlherr and W.D.Neumann.Comment: Part 1 of

Minimality of the boundary of a right-angled Coxeter system

In this paper, we show that the boundary $\partial\Sigma(W,S)$ of a right-angled Coxeter system $(W,S)$ is minimal if and only if $W_{\tilde{S}}$ is irreducible, where $W_{\tilde{S}}$ is the minimum parabolic subgroup of finite index in $W$. We also provide several applications and remarks. In particular, we obtain that for a right-angled Coxeter system $(W,S)$, the set $\{w^{\infty} | w\in W, o(w)=\infty\}$ is dense in the boundary $\partial\Sigma(W,S)$

On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature

In this paper, we show some splitting theorems for CAT(0) spaces on which a product group acts geometrically and we obtain a splitting theorem for compact geodesic spaces of non-positive curvature. A CAT(0) group $\Gamma$ is said to be {\it rigid}, if $\Gamma$ determines the boundary up to homeomorphisms of a CAT(0) space on which $\Gamma$ acts geometrically. C.Croke and B.Kleiner have constructed a non-rigid CAT(0) group. As an application of the splitting theorems for CAT(0) spaces, we obtain that if $\Gamma_1$ and $\Gamma_2$ are rigid CAT(0) groups then so is $\Gamma_1\times \Gamma_2$.Comment: 14 page

Coxeter systems with two-dimensional Davis-Vinberg complexes

In this paper, we study Coxeter systems with two-dimensional Davis-Vinberg complexes. We show that for a Coxeter group $W$, if $(W,S)$ and $(W,S')$ are Coxeter systems with two-dimensional Davis-Vinberg complexes, then there exists $S''\subset W$ such that $(W,S'')$ is a Coxeter system which is isomorphic to $(W,S)$ and the sets of reflections in $(W,S'')$ and $(W,S')$ coincide. Hence the Coxeter diagrams of $(W,S)$ and $(W,S')$ have the same number of vertices, the same number of edges and the same multiset of edge-labels. This is an extension of results of A.Kaul and N.Brady, J.P.McCammond, B.M\"uhlherr and W.D.Neumann

On a new class of rigid Coxeter groups

In this paper, we give a new class of rigid Coxeter groups. Let $(W,S)$ be a Coxeter system. Suppose that (0) for each $s,t\in S$ such that $m(s,t)$ is even, $m(s,t)\in\{2\}\cup 4\N$, (1) for each $s\neq t\in S$ such that $m(s,t)$ is odd, $\{s,t\}$ is a maximal spherical subset of $S$, (2) there does not exist a three-points subset $\{s,t,u\}\subset S$ such that $m(s,t)$ and $m(t,u)$ are odd, and (3) for each $s\neq t\in S$ such that $m(s,t)$ is odd, the number of maximal spherical subsets of $S$ intersecting with $\{s,t\}$ is at most two, where $m(s,t)$ is the order of $st$ in the Coxeter group $W$. Then we show that the Coxeter group $W$ is rigid. This is an extension of a result of D.Radcliffe.Comment: Part 3 of

On the semi-direct product structure of CAT(0) groups

In this paper, we investigate finitely generated groups of isometries of CAT(0) spaces containing some central hyperbolic isometry, and study CAT(0) groups. We show that every CAT(0) group $\Gamma$ has the semi-direct product structure $\Gamma=(\cdots(((\Gamma'\rtimes\langle\delta_{n}\rangle)\rtimes\langle\delta_{n-1}\rangle)\rtimes\langle\delta_{n-2}\rangle)\cdots)\rtimes\langle\delta_{1}\rangle$ where $\Gamma'$ is a CAT(0) group with finite center and $\delta_i\in \Gamma$ for $i=1,\dots,n$, and $\Gamma$ contains a finite-index subgroup $\Gamma'\times A$ where $A$ is isomorphic to ${\mathbb{Z}}^n$. We introduce some examples and remarks. Also we provide an example of a virtually irreducible CAT(0) group with trivial-center that acts geometrically on some CAT(0) space that splits as a product $T \times {\mathbb{R}}$.Comment: This paper has been withdrawn by the author due to a crucial error in the example of a virtually irreducible CAT(0) group with trivial-center that acts geometrically on some CAT(0) space that splits as a product $T \times {\mathbb{R}}

Statistical Mechanical Approach to Lossy Data Compression:Theory and Practice

The encoder and decoder for lossy data compression of binary memoryless sources are developed on the basis of a specific-type nonmonotonic perceptron. Statistical mechanical analysis indicates that the potential ability of the perceptron-based code saturates the theoretically achievable limit in most cases although exactly performing the compression is computationally difficult. To resolve this difficulty, we provide a computationally tractable approximation algorithm using belief propagation (BP), which is a current standard algorithm of probabilistic inference. Introducing several approximations and heuristics, the BP-based algorithm exhibits performance that is close to the achievable limit in a practical time scale in optimal cases.Comment: 10 pages, 2 figures, REVTEX preprin

Negative Parity Baryons in the QCD Sum Rule

Masses and couplings of the negative parity excited baryons are studied in the QCD sum rule. Separation of the negative-parity spectrum is proposed and is applied to the flavor octet and singlet baryons. We find that the quark condensate is responsible for the mass splitting of the ground and the negative-parity excited states. This is expected from the chiral symmetry and supports the idea that the negative-parity baryon forms a parity doublet with the ground state. The meson-baryon coupling constants are also computed for the excited states in the QCD sum rule. It is found that the \pi NN^* coupling vanishes in the chiral limit.Comment: 13pp, LaTeX, 1 EPS figure, uses epsf.sty, Talk given by M.O. at CEBAF/INT workshop "N* physics", Seattle, September (1996), to appear in the proceeding