On the quantization of SU(3) skyrmions

The quantization condition derived previously for SU(2) solitons quantized with SU(3) collective coordinates is generalized for SU(3) skyrmions with nonzero strangeness content. Quantization of the recently discovered dipole-type configuration with large strangeness content is considered as an example. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 391–396 (25 September 1996) This study was supported by the Russian Fund for Fundamental Research, Grant 95-02-03868a and by Volkswagenstiftung, FRG. Published in English in the original Russian journal. Edited by Steve Torstveit.     

Algebraic quantization of the SU(3) skyrmion

The algebraic quantization of the SU(3) skyrmion is presented. We discuss the role of the number of colors (N_c) in QCD and the Wess-Zumino term in the quantization. Two distinct dynamical group chains are shown to correspond to different methods of semiclassical quantization. We obtain most of the SU(6) quark model predictions for the skyrmion quantized with N_c=3.     

Semiclassical quantization of the supermembrane

We approach the quantization of the eleven-dimensional supermembrane from a semiclassical viewpoint. We quantize the fluctuations around a topologically-stabilized toroidal background, and find that the bosonic and fermionic contributions to the vacuum energy cancel. This result appears to depend crucially on the fermionic gauge symmetry and spacetime supersymmetry.     

Semiclassical quantization rules near separatrices

We derive semiclassical quantization equations with uniform estimate of the error term near unstable equilibria of the classical system for the one-dimensional Schrödinger operator.     

Semiclassical quantization of relative skyrmion-skyrmion motion

The relative motion of the two-skyrmion system is quantized semiclassically. The reduced mass is calculated as a function of the relative distance and a large enhancement is seen at short distances. An effective momentum-dependent interaction is discussed quantitatively.     

SU (4) × SU (4) symmetry breaking and its implications for SU (3) × SU (3) breaking

We investigate models where the SU (4) × SU (4) symmetry breaking Hamiltonian, $\text{H}$_SB, belongs to the (15, 15) and $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ representations, and show how they are equivalent to models of SU (3) × SU (3) breaking where $\text{H}$_SB belongs to a mixture of different representations. The results for the ππ scattering lengths in the (15, 15) model are outside the experimental limits, but the $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ model yields solutions with a wide range of values for the scattering lengths within the experimental bounds.     

Semiclassical quantization of the Bogoliubov spectrum

We analyze the Bogoliubov spectrum of the three-site Bose-Hubbard model with a finite number of Bose particles by using a semiclassical approach. The Bogoliubov spectrum is shown to be associated with the low-energy regular component of the classical Hubbard model. We identify the full set of the integrals of motion of this regular component and, quantizing them, obtain the energy levels of the quantum system. The critical values of the energy, above which the regular Bogoliubov spectrum evolves into a chaotic spectrum, is indicated as well.     

Semiclassical quantization of the shell model

The classical limit of the nuclear shell model is shown to be a many-dimensional hamiltonian system in which the coordinates and momenta are the coherent-state parameters of the original quantum system. Several methods for semiclassical quantization of this system are discussed, including surfaces of section and the Birkhoff-Gustavson transformation to action-angle variables. Application to a schematic three-level shell model indicates some of the new problems involved in requantizing multi-dimensional systems which are not present in one-dimensional examples. These include difficulties in finding periodic orbits and the onset of stochasticity.     

半经典近似:混沌运动的量子化

早期量子论的玻尔－索末菲规则对混沌运动失效,新的半经典近似从能级、本征态和状态的时间演化三个范畴上探讨了混沌运动的量子化,从而发展了“近代后量子力学”。     

Is the SU(3) pattern evidence for SU(3) symmetry?

The results obtained in this paper show that the SU(3) pattern in the spectra and transition rates of even-even nuclei appear qualitatively as a general feature of a large class of quadrupole-phonon models, independently of SU(3) symmetry. This pattern reflects the truncation of the quadrupole phonon space, incorporated via truncation operator in the fourth-order anharmonic quadrupole-phonon Hamiltonian. Three particular forms of the truncation operator are considered, corresponding to three models, namely the truncated quadrupole-phonon model (TQM), equivalent to the well-known interacting-boson model (IBM), the step-truncated quadrupole-phonon model (STQM), equivalent to a standard anharmonic quadrupole-phonon model and the linearly truncated quadrupole-phonon model (LTQM), introduced here. The results obtained provide a basis for a broader scope for the considerations in the SU(3) limit.