Incompleteness of Representation Theory: Hidden symmetries and Quantum Non-Integrability

Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of these hidden symmetries depends upon the realization of the Hamiltonian.Comment: 4 pages, Revtex, Phys. Rev. Lett. , July 27 (1997), in pres

Transport parameters in neutron stars from in-medium NN cross sections

We present a numerical study of shear viscosity and thermal conductivity of symmetric nuclear matter, pure neutron matter and $\beta$-stable nuclear matter, in the framework of the Brueckner theory. The calculation of in-medium cross sections and nucleon effective masses is performed with a consistent two and three body interaction. The investigation covers a wide baryon density range as requested in the applications to neutron stars. The results for the transport coefficients in $\beta$-stable nuclear matter are used to make preliminary predictions on the damping time scales of non radial modes in neutron stars

N K Pi molecular state with I=1 and J(Pi)=3/2-

The structure of the molecule-like state of $NK\pi$ with spin-parity $J^{\pi}={3/2}^-$ and isospin I=1 is studied within the chiral SU(3) quark model. First we calculate the $NK$, $N\pi$, and $K\pi$ phase shifts in the framework of the resonating group method (RGM), and a qualitative agreement with the experimental data is obtained. Then we perform a rough estimation for the energy of $(NK\pi)_{J^{\pi}={3/2}^-,I=1}$, and the effect of the mixing to the configuration $(\Delta K)_{J^{\pi}={3/2}^-,I=1}$ is also considered. The calculated energy is very close to the threshold of the $NK\pi$ system. A detailed investigation is worth doing in the further study.Comment: 11 pages, 3 figures; accepted for publication in Phys. Rev.

Resonating group method study of kaon-nucleon elastic scattering in the chiral SU(3) quark model

The chiral SU(3) quark model is extended to include an antiquark in order to study the kaon-nucleon system. The model input parameters $b_u$, $m_u$, $m_s$ are taken to be the same as in our previous work which focused on the nucleon-nucleon and nucleon-hyperon interactions. The mass of the scalar meson $\sigma$ is chosen to be 675 MeV and the mixing of $\sigma_0$ and $\sigma_8$ is considered. Using this model the kaon-nucleon $S$ and $P$ partial waves phase shifts of isospin I=0 and I=1 have been studied by solving a resonating group method (RGM) equation. The numerical results of $S_{01}$, $S_{11}$, $P_{01}$, $P_{03}$, and $P_{11}$ partial waves are in good agreement with the experimental data while the phase shifts of $P_{13}$ partial wave are a little bit too repulsive when the laboratory momentum of the kaon meson is greater than 500 MeV in this present calculation.Comment: 17 pages, 6 figures. Final version for publicatio

Baryon-meson interactions in chiral quark model

Using the resonating group method (RGM), we dynamically study the baryon-meson interactions in chiral quark model. Some interesting results are obtained: (1) The Sigma K state has an attractive interaction, which consequently results in a Sigma K quasibound state. When the channel coupling of Sigma K and Lambda K is considered, a sharp resonance appears between the thresholds of these two channels. (2) The interaction of Delta K state with isospin I=1 is attractive, which can make for a Delta K quasibound state. (3) When the coupling to the Lambda K* channel is considered, the N phi is found to be a quasibound state in the extended chiral SU(3) quark model with several MeV binding energy. (4) The calculated S-, P-, D-, and F-wave KN phase shifts achieve a considerable improvement in not only the signs but also the magnitudes in comparison with other's previous quark model study.Comment: 5 pages, 2 figures. Talk given at 3rd Asia Pacific Conference on Few-Body Problems in Physics (APFB05), Korat, Nakhon Ratchasima, Thailand, 26-30 Jul 200

Cocommutative Calabi-Yau Hopf algebras and deformations

The Calabi-Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group algebra of a universal enveloping algebra of a finite dimensional Lie algebra \g with a finite subgroup $G$ of automorphisms of \g is Calabi-Yau if and only if the universal enveloping algebra itself is Calabi-Yau and $G$ is a subgroup of the special linear group SL(\g). The Noetherian cocommutative Calabi-Yau Hopf algebras of dimension not larger than 3 are described. The Calabi-Yau property of Sridharan enveloping algebras of finite dimensional Lie algebras is also discussed. We obtain some equivalent conditions for a Sridharan enveloping algebra to be Calabi-Yau, and then partly answer a question proposed by Berger. We list all the nonisomorphic 3-dimensional Calabi-Yau Sridharan enveloping algebras