18113451
Symplectic, multisymplectic structures and Euler-Lagrange cohomology
We study the Euler-Lagrange cohomology and explore the symplectic or multisymplectic geometry and their preserving properties in classical mechanism and classical field theory in Lagrangian and Hamiltonian formalism in each case respectively. By virtue of the Euler-Lagrange cohomology that is nontrivial in the configuration space, we show that the symplectic or multisymplectic geometry and related preserving property can be established not only in the solution space but also in the function space if and only if the relevant closed Euler-Lagrange cohomological condition is satisfied in each case. We also apply the cohomological approach directly to Hamiltonian-like ODEs and Hamiltonian-like PDEs no matter whether there exist known Lagrangian and/or Hamiltonian associated with them.
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.
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.
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.
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.