124440265
QUANTUM GROUPS AND SPECTRA OF DIATOMIC-MOLECULES
We briefly review and further investigate the quantum group theoretic approach to the spectra of the diatomic molecules presented by the authors recently. The vibration-rotational structures as well as the interactions of vibrations and rotations are described in the quantum group theoretic approach satisfactorily. When Taylor expanded, the analytic formulae of the new approach reproduce the results of nonlinear vibrating rotator model. For some particular states of randomly selected molecules, the parameters of the new approach are computed to fit the phenomenological data to high accuracies. We also supply an analysis of the (pseudo-) potential implied in the new model, and compare it with the conventional model of the local potential that is applied in the explanation of the Dunham formula of energy spectra.
123221609
The Topolosical Origins of Gauge Anomalies
In addition to the recent discovery that the Chern-Simons secondary classes are the topological origins generating special unitary gauge group anomalies, it is shown that some special orthogonal gauge group anomalies can also be generated, from the Pontrjagin and the Euler secondary classes. The common differential geometrical and topological background are explained as well.
124706747
THE COMPACT ALGEBRA STRUCTURE OF SOLITON-EQUATIONS, THEIR SPINOR AKNS SYSTEM AND REALIZATION ON SPHERE
Abstract It is shown that a great sort of soliton equations, such as sine- Gordon equation and others whose inverse scattering problem is described by the AKNS system, has both noncompact and compact algebra structures on the same footing. The spinor AKNS system and realization on sphere with respect to the compact structure of the soliton equations are given.
123188834
Inverse Scattering Transform and Regular Riemann-Hilbert Problem
It is shown that the inverse scattering transform method for solving the Lax pair of given nonlinear evolution equation can be reduced to a kind of Riemann-Hilbert (RH) problem of meromorphic functions with respect to the complex spectral parameter. The RH problem is generally regular no matter solitons are involved or not. The linear singular integral equation associated with the RH problem has been derived, which is essential1y equivalent to the Gellfand-Levitan-Marchenko equation. Furthermore, the regullar RH problem satisfied by the Backlund transformation from a fundamental solution set of the eigenvalue equations of Lax pair to a new set has Fen given as well. The RH problem reduced from the inverse scattering transform is in fact a special case of that satisfied by the Backlund transformation.
16213964
Quantization of Chern-Simons coefficient
The relation between the Dirac quantization condition of magnetic charge and the quantization of the Chern-Simons coefficient is obtained. It implies that in a (2+1)-dimensional QED with the Chern-Simons topological mass term and the existence of a magnetic monopole with magnetic charge g, the Chern-Simons coefficient must also be quantized, just as in the non-Abelian case.
124798738
DIFFEOMORPHISM AND BELTRAMI ALGEBRAS ON TORUS
The infinite-dimensional algebras on two-dimensional torus are developed. In particular the diffeomorphism algebra and the Beltrami algebra on torus with their central extensions have been presented. It is shown that these algebras are corresponding to the diffeomorphism and the quasiconformal transformation of torus, respectively.
55378666
Analysis of chiral symmetry breaking mechanism
— The renormalization group invariant quark condensate m× is determined both from the consistent equation for quark condensate in the chiral limit and from the Schwinger-Dyson (SD) equation improved by the intermediate range QCD force singular like d(q) which is associated with the gluon condensate. The solutions of m× in these two equations are consistent. We also obtain the critical strong coupling constant a c above which chiral symmetry breaks in these two approaches. The nonperturbative kernel of the SD equation makes a c smaller and m× bigger. An intuitive picture of the condensation above a c is discussed. In addition, with the help of the Slavnov-Taylor-Ward (STW) identity we derive the equations for the nonperturbative quark propagator from the SD equation in the presence of the intermediate range force and find that the intermediate-range force is also responsible for dynamical chiral symmetry breaking.