含Hopf项和Maxwell-Chern-Simons项O(3)非线性σ模型的分数自旋和分数统计性质

研究了（2＋1）维时空中含Hopf项和Maxwell-Chern-Simons(MCS)项的非线性σ模型的分数自旋性质.根据约束Hamilton系统的Faddeev-Senjanovic(FS)路径积分量子化方案,对该系统进行量子化，由量子Noether定理给出了量子守恒角动量，说明了在量子水平上该系统仍具有分数自旋的性质. 关键词： 约束Hamilton系统 分数自旋 O(3)σ模型     

Hopf term,fractional spin and soliton operators in the O(3) non-linear sigma model

We re-examine three issues, the Hopf term, fractional spin and the soliton operators, in the 2+1 dimensional O(3) non-linear sigma model based on the adjoint orbit parametrization (AOP) introduced earlier. It is shown that the Hopf term is well defined for configurations of any soliton charge Q if we adopt a time-independent boundary condition at spatial infinity. We then develop the Hamiltonian formulation of the model in the AOP and thereby argue that the well-known Q² formula for fractional spin holds only for a restricted class of configurations. Operators that create states of given classical configurations of any soliton number in the (physical) Hilbert space are constructed. Our results clarify some of the points that are crucial for the above three topological issues and yet have remained obscure in the literature.     

Topological features of the nonlinear sigma model with Hopf term using chiral lagrangians

We rewrite the O(3) nonlinear sigma model in 2 + 1 dimensions in terms of SU(2) matrices, thereby solving the constraint. The lagrangian has the symmetry SU(2)_Global×U(1)_Local. Static soliton solutions to this lagrangian have energy 4πN as usual. We then show that the Hopf instantons, in the formalism of principle chiral fields, are just the skymions of QCD in 3 + 1 dimensions.     

Mass spectrum of the two-dimensional O(3) sigma model with a theta term

Form factor perturbation theory is applied to study the spectrum of the O(3) nonlinear sigma model with the topological term in the vicinity of theta=pi. Its effective action near this value is given by the nonintegrable double sine-Gordon model. Using previous results by Affleck and the explicit expressions of the form factors of the exponential operators e(+/-isqrt[8pi]phi(x)), we show that the spectrum consists of a stable triplet of massive particles for all values of theta and a singlet state of higher mass. The singlet is a stable particle only in an interval of values of theta close to pi, whereas it becomes a resonance below a critical value theta(c).     

A numerical study of the RG equation for the deformed O(3) nonlinear sigma model

The Renormalization Group equation describing the evolution of the metric of the nonlinear sigma model poses some nice mathematical problems involving functional analysis, differential geometry and numerical analysis. In this article we briefly report some results obtained from the numerical study of the solutions in the case of a two-dimensional target space (deformation of the O(3) σ-model In particular, our analysis shows that the so-called sausages define an attracting manifold in the U(1)-symmetric case, at one-loop level. Moreover, data from two-loop evolution are used to test the association (Fateev, Onofri and ALB. Zamolodchikov, Nucl. Phys. B 406 (1993) 521) between the so-called SSM_η field theory and a certain U(1)-symmetric, factorized scattering theory (FST).