Symmetries of a (2+1)-Dimensional Toda-like Lattice

Lie group technique for solving differential-difference equations is applied to a new (2 1)-dimensional Toda-like lattice. An infinite dimensional Lie algebra and the corresponding commutation relations are obtained.     

Symmetries of a （2＋1）-Dimensional Toda-like Lattice

Lie group technique for solving differential-difference equations is applied to a new (2 1)-dimensional Toda-like lattice. An infinite dimensional Lie algebra and the corresponding commutation relations are obtained.     

Dyonic Sectors and Intertwiner Connections in 2+1-Dimensional Lattice -Higgs Models

We construct dyonic states in 2+1-dimensional lattice -Higgs models, i.e. states which are both, electrically and magnetically charged. These states are parametrized by , where ɛ and μ are -valued electric and magnetic charge distributions, respectively, living on the spatial lattice . The associated Hilbert spaces carry charged representations of the observable algebra , the global transfer matrix t and a unitary implementation of the group of spatial lattice translations. We prove that for coinciding total charges these representations are dynamically equivalent and we construct a local intertwiner connection , where is a path in the space of charge distributions . The holonomy of this connection is given by -valued phases. This will be the starting point for a construction of scattering states with anyon statistics in a subsequent paper. Received: 13 December 1996 / Accepted: 19 May 1997     

Decomposition for a 2+1-Dimensional Discrete Integrable Model

A 2＋1-dimensional discrete is presented, which is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems, with aid of the nonlineaxization of Lax pairs. The system is completely integrable in the Liouville sense.     

SU(2) Lattice Gauge Theory Formulation of the (2+1)-Dimensional Antiferromagnetic Heisenberg Model

The equivalence of 2+1 antiferromagnetic Heisenberg model and the SU(2) Kogut Susskind lattice gauge theory is recapitulated and the naive Euclidean lattice action of the threedimensional an tiferromagnetic Heisen berg model is derived. The three-dimensional lattice gauge fermion theory is formulated to give the consistent lattice gauge theory of antiferromagnetic Heisenberg model. In continu um limit the two copies of two flavor fermions are resulted, which give the negative results of the microscopic derivation of the Chern-Simons terms. The Chern-Simons terms, the gauge invariant problem of effective action and the '%hiralityn are discussed.     

Phase Transition and Critical Behavior for XY Model on 2-Dimensional Random Triangle Lattice

The Monte Carlo renormalization group method is applied to discussing the nature of phase transition of XY model on 2-dimensional random triangle lattices. A line of fixed point and un-universal phase transition are found. The results are in agreement with Kosterlitz-Thouless theory. The susceptibility ehows a clear size-dependent behaviorin low temperature region. This means that it should be divergent in this region.     

Explicit Solutions for a （2＋1）-Dimensional Toda Lattice with Two Discrete Variables

An integrable （2＋1）-dimensional Toda lattice with two discrete variables is investigated again, which is produced from a compatible condition of the Lax triad. The Darboux transformation for its spectral problems is found. As an application, explicit solutions of the （2＋1）-dimensional Toda equation with two discrete variables are obtained.     

A 7-Dimensional Model of Gravielectroweak Interactions as a Corollary of an 8-Dimensional Model

A geometric model for uniting gravitational, strong, and electroweak physical interactions within the framework of an 8-dimensional theory of the Kaluza–Klein type is proposed. It is shown that strong and electroweak interactions of quarks can be understood as special cases of manifestation of an 8-dimensional geometry reduced to a 4-dimensional theory.     

2+1维U(1)格点规范场论中真空态的研究

对2+1维U(1)格点规范场论真空态进行研究,仔细推导出连续极限下真空谈函数中参数μ₀和μ₂的普适表达式,并用截断本征方程法进行数值计算.     

On （2＋1）-Dimensional Non-isospectral Toda Lattice Hierarchy and Integrable Coupling System

By considering （2＋1）-dimensional non-isospectral discrete zero curvature equation, the （2＋1）-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of the （2＋1）- dimensional Toda lattice hierarchy are given. Finally, the （2＋1）-dimensional integrable coupling system of the Toda lattice hierarchy is obtained through enlarging spectral problem.     

Independent Plaquette Trial Action for 4-Dimensional Lattice Gauge Theory

Based on the explicit expressions of the plaquette formulations, the independent plaquette trial action for 4-dimensional lattice gauge theory is introduced. As an example, the mean plaquette energy EP for the SU(2) lattice gauge theory is calculated by using action variational approach with the independent trial action. The results are in good agreement with the Monte Carlo results in the strong coupling and the crossover region, and the curve is smooth in the whole region, which show that 4-dimensional SU(2) theory has only a single, confining phase. The unwanted discontinuity of EP given by the single link trial action, which is used in the earlier variational calculations has been avoided.     

Hierarchy of Combined TL-RTL Equations and an Associated (2+1)-Dimensional Lattice Equation

A new (2+1)-dimensional lattice equation is presented based upon the first two members in the hierarchy of the combined Toda lattice and relativistic Toda lattice (TL-RTL) equations in (1+1) dimensions. A Darboux transformation for the hierarchy of the combined TL-RTL equations is constructed. Solutions of the first two members in the hierarchy of the combined TL-RTL equations, as well as the new (2+1)-dimensional lattice equation are explicitly obtained by the Darboux transformation.     

Hierarchy of Combined TL-RTL Equations and an Associated (2+1)-Dimensional Lattice Equation

A new (2 1)-dimensional lattice equation is presented based upon the first two members in the hierarchy of the combined Toda lattice and relativistic Toda lattice (TL-RTL) equations in (1 1) dimensions. A Darboux transformation for the hierarchy of the combined TL-RTL equations is constructed. Solutions of the first two members in the hierarchy of the combined TL-RTL equations, as well as the new (2 1)-dimensional lattice equation are explicitly obtained by the Darboux transformation.     

2+1维SU(3)格点纯规范场的真空态计算

用连续极限截断的格点本征值方法^[1],研究2+1维SU(3)的格点规范理论的真空态.在强耦合区,上述方法的结果与强耦合展开一致.在过渡区,上述方法的结果显示出较好的标度行为.     

A Model of the Electron in a 6-Dimensional Spacetime

The electron is considered as a massless point-particle which moves in a spacetime with (3+3) dimensions subjected to a field that attracts it towards the (3+1) standard spacetime. This field is assumed to be described by the radial time component of the e.m. 6-potential and to be due to the vacuum polarization arising when the charge of the electron is removed from the (3+1) spacetime. The pertinent Klein-Gordon equitation in 6 dimensions is solved and the right values for the electron magnetic moment and spin are derived. The rest mass of the electron, as it appears in the standard (3+1) spacetime, is obtained as an integration constant from the motion in the two extra time dimensions. The very simple form assumed as a first approximation for the attractive potential does not give quantized rest masses.     

An Anyon Model in a Toric Honeycomb Lattice

We study an anyon model in a toric honeycomb lattice. The ground states and the low-lying excitations coincide with those of Kitaev toric code model and then the excitations obey mutual semionic statistics. This model is helpful to understand the toric code of anyons in a more symmetric way. On the other hand, there is a direct relation between this toric honeycomb model and a boundary coupled Ising chain array in a square lattice via Jordan-Wignertransformation. We discuss the equivalence between these two modelsin the low-lying sector and realize these anyon excitations in a conventional fermion system. The analysis for the ground state degeneracy in the last section can also be thought of as a complementarity of our previous work [Phys. A: Math. Theor. 43 (2010) 105306].     

Multivortex Solutions in (2+1)-Dimensional Abelian Higgs Model with a Chern-Simons Term

The multivortex solutions of (2+l)-dimensional Abelian Higgs model with a Chern-Simons term are stlrrlied. The Bogomol'nyi-type equations and corresponding Weinberg's index theorem have been derived for a sixth-order Higgs potential. The magnetic field is different from that of the Abelian Chern-Simons Higgs model which has no Maxwell term, and has a maximum at the center of the vortex.