磁场诱导的单离子各向异性反铁磁链的比热

利用改进的Schwinger玻色子平均场理论,研究了横向外加磁场下自旋为1的单粒子各向异性海森堡反铁磁链的热力学性质.发现在外加磁场下预示这一体系中存在Luttinger液体相—完全极化相相变的比热奇性,并给出了相应的相图.研究还发现,单粒子各向异性对比热的影响较小,这和纵向场的结果完全不同.以上结果对整自旋的反铁磁链具有普适性,对实验研究具有指导性. 关键词： 反铁磁链 热力学性质 Schwinger 玻色子     

Relativistically Covariant Quantum Field Theory of the Maslov Complex Germ

We consider an explicitly covariant formulation of the quantum field theory of the Maslov complex germ (semiclassical field theory) in the example of a scalar field. The main object in the theory is the “semiclassical bundle” whose base is the set of classical states and whose fibers are the spaces of states of the quantum theory in an external field. The respective semiclassical states occurring in the Maslov complex germ theory at a point and in the theory of Lagrangian manifolds with a complex germ are represented by points and surfaces in the semiclassical bundle space. We formulate semiclassical analogues of quantum field theory axioms and establish a relation between the covariant semiclassical theory and both the Hamiltonian formulation previously constructed and the axiomatic field theory constructions Schwinger sources, the Bogoliubov S-matrix, and the Lehmann-Symanzik-Zimmermann R-functions. We propose a new covariant formulation of classical field theory and a scheme of semiclassical quantization of fields that does not involve a postulated replacement of Poisson brackets with commutators.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 3, pp. 492–512, September, 2005.     

Motives associated to graphs

A report on recent results and outstanding problems concerning motives associated to graphs. This article is based on the 1st Takagi Lectures that the author delivered at Research Institute for Mathematical Sciences, Kyoto University on November 25 and 26, 2006.     

一维Lippmann-Schwinger方程及其应用

讨论了一维Lippmann-Schwinger方程及其在一维散射问题中的应用,并给出了对称害虫函数势的反射系数和透射系数。     

Interacting Theory of Chiral Bosons and Gauge Fields on Noncommutative Extended Minkowski Spacetime

Several interacting models of chiral bosons and gauge fields are investigated on the noncommutative extended Minkowski spacetime which was recently proposed from a new point of view of disposing noncommutativity. The models include the bosonized chiral Schwinger model, the generalized chiral Schwinger model (GCSM) and its gauge invariant formulation. We establish the Lagrangian theories of the models, and then derive the Hamilton's equations in accordance with the Dirac's method and solve the equations of motion, and further analyze the self-duality of the Lagrangian theories in terms of the parent action approach.     

Studies on the Chiral Order Parameter in the Schwinger Model

Based on an analytical technique using a unitary transformation and the variational method, we study the chiral order parameter in the Schwinger model in the lattice formalism with Kogut-Susskind fermions. The fermion condensate (ψψ)fo r any coupling constant and fermion mass are calculated. Chiral symmetry is shown to be broken in the massless limit and good scaling behavior is obtained.