Exact (1+1)-dimensional solutions of discrete planar velocity Boltzmann models

For discrete velocity Boltzmann models we have found (1+1)-dimensional shock waves and periodic solutions that are rational solutions with two exponential variables exp(_ix + _it) (spacex, timet). These exact solutions are sums of two rational solutions, each with one exponential variable (similarity solutions). We study the planar velocity models and explicitly write the results for the square 4-velocity and the hexagonal 6-velocity models introduced by Gatignol.     

d-Dimensional hubbard model as a (d + 1)-dimensional classical problem

We show an exact equivalence between the partition function of a d-dimensional model of electrons with short range interactions and a (d + 1)-dimensional classical problem. For d = 1 the latter is the combinatorial problem of two coupled arrow-vertex models.     

（2+1）维耗散长波方程与(2+1)维Broer-Kaup方程新的类多孤子解

进一步拓广齐次平衡法的应用，并对关键的操作步骤进行了改进，从而简便地求出了（2+1 ）维耗散长波方程和（2+1）维Broer-Kaup方程新的类多孤子解-这种解更具有一般性，它包 含着已有文献给出的类多孤子解- 关键词： 齐次平衡法 类多孤子解 （2+1）维耗散长波方程 （2+1）维Broer-Kaup方程     

Renormalization of the casimir energy in the (1+1)-dimensional fermion-bag models

The ground-state energy in the two-phase hybrid chiral fermion-bag model involving boson-fermion interaction is studied in (1+1)-dimensional spacetime. A procedure for renormalizing the divergent energy of the fermion sea is proposed. The procedure is based on the isolation of singular terms and the subsequent absorption of these divergences in the redefined parameters of the input Lagrangian.     

Non-perturbative renormalization group functions in (2+1)-dimensional supersymmetric gauge theories

Three-dimensional supersymmetric Higgs models with an additional U(N) flavor symmetry are considered within the 1/N expansion. Explicit expressions for the renormalization group functions are obtained in the large N limit which exhibit logarithmic dependence on the gauge coupling constants.     

（2＋1）维sine—Gordon方程的三种函数混合解

基于一构造的Wronskian形式展开法，获得了（2＋1）维sine—Gordon方程的一系列新形式的混合解．这些解是三角函数、双曲函数及Jacobi椭圆函数等三种函数的组合形式．     

Phase transition and 1/N expansion in (2+1)-dimensional supersymmetric sigma models

Three-dimensional supersymmetric generalized non-linear sigma models are shown to exhibit second-order phase transition due to spontaneous breakdown of the internal symmetry below a critical value of the coupling constant. Supersymmetry remains unbroken in both phases. Supergraph diagram technique of the corresponding 1/N expansion and the particle spectrum are derived.     

Exact form factors in (1 + 1)-dimensional field theoretic models with soliton behaviour

A system of equations is derived which must be satisfied by multiparticle matrix elements of any local operator in field theories with soliton behaviour. Form factors of various operators of interest are calculated exactly by means of the known exact S-matrices in the sine-Gordon, massive Thirring, non-linear σ^?, and Gross-Neveu models. The finite sine-Gordon wave function renormalization constant is determined exactly.     

Supergravity in (2 + 1) dimensionsfrom (3 + 1)-dimensional supergravity

In the context of the formalism proposed by Stelle-West and Grignani-Nardelli, it is shown that Chern-Simons supergravity can be consistently obtained as a dimensional reduction of (3 + 1)-dimensional supergravity, when written as a gauge theory of the Poincaré group. The dimensional reductions are consistent with the gauge symmetries, mapping (3 + 1)-dimensional Poincaré supergroup gauge transformations onto (2 + 1)-dimensional Poincaré supergroup ones.     

The point-splitting regularization of (2+1)d parity breaking models

The coefficient of the Chern–Simons term in the effective action for massive Dirac fermions in three dimensions is computed by using the point-splitting regularization method. We show that in this framework no ambiguities arise. This is related to the fact that the point-splitting regularization does not introduce additional parity breaking effects, implementing one possible physical criterion in order to uniquely characterize the system.     

Construction of positive exact (2+1)-dimensional shock wave solutions for two discrete Boltzmann models

It is proved that (2+1)-dimensional (spacex, y; timet) positive exact shock wave solutions of two discrete Boltzmann models exist. For each densityN _i, these solutions are linear combinations of three similarity shock waves,N _i =n _0i + _j n _ji /[1+d _j exp( _j y+y _j x+ _j t)],j=1,2,3. Two models with four independent densities are investigated: the square discrete-velocity Boltzmann model and the model with eight velocities oriented toward the eight corners of a cube.The positivity problem for the densities is nontrivial. Two classes of solutions are considered for which the two first similarity shock wave components depend on only one spatial dimension, _j=const· _j ,j=1,2. For the positivity, if ₁₂>0, it is sufficient to prove that the 16 asymptotic shock limitsn _0i ,n _0i +n _3i , _j=0 ² n _ji , _j=0 ³ n _ji are positive. The density solutions are built up with five arbitrary parameters and we prove that there exist subdomains of the arbitrary parameter space in which the 16 shock limits are positive. We study numerically two explicit shock wave solutions. We are interested in the movement of the shock front when the time is growing and in the possible appearance of bumps. In the space, at intermediate times, these bumps represent populations of particles which are larger than at initial time or at equilibrium time.     

Teleparallel equivalent theory of (1+1)-dimensional gravity

A theory of (1+1)-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity.The fundamental field variables are the tetrad fields e i μ and the gravity is attributed to the torsion.A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived.The energy associated with this solution is calculated using the two-dimensional gravitational energy-momentum formula.