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.
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.
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.
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.
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.
16106369
The Euler–Lagrange Cohomology and General Volume-Preserving Systems
We briefly introduce the concept of Euler–Lagrange cohomology groups on a symplectic manifold (ℳ2n, ω) and systematically present the general form of volume-preserving equations on the manifold from the cohomological point of view. It is shown that for every volume-preserving flow generated by these equations there is an important two-form that plays the analog role with the Hamiltonian in the Hamilton mechanics. In addition, the ordinary canonical equations with Hamiltonian H are included as a special case with the two-form . The other volume preserving systems on (ℳ2n, ω) are studied. The relations between our approach and Feng–Shang's volume-preserving systems as well as the Nambu mechanics are also explored.
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.