Renormalization group and dynamical symmetry breakdown in abelian gauge theories

Generalized renormalization group equations are used to analyze the dynamical mechanism of particle mass generation in terms of the Cornwall-Norton model both with and without cut-off. We look for solutions which contain non-zero physical masses of the two fermions (m₁, m₂) and of one of the vector bosons (μ) when the bare masses m_1Λ, m_2Λ, μ_Λ approach zero. For a theory without cut-off we obtain results which are similar to those of Cornwall. For a theory with cut-off the mass generation mechanism may only occur when a bare coupling constant α_Λ of the A_μ vector boson, which remains massless, exceeds some critical value α_c. In this case the fermion masses turn out to be of the superconductivity type.The model's “memory” of the nature of spontaneous symmetry breaking lim_{m1Λ, m2Λ → 0}m_1Λ/m_2Λ ≠ 1 is an indispensible factor for the vector boson to acquire a mass.     

Chiral-symmetry breakdown and the spectrum of pseudoscalar mesons in quantum chrompdynamics

Using the dynamical equations which describe both spontaneous and explicit chiral-symmetry breakdown in chromodynamics the mass relations for the pseudoscalar nonet are obtained.     

On the dynamical vacuum rearrangement and the problem of fermion mass generation

We discuss the conditions under which the dynamical fermion mass generation mechanism may occur. The analogy between the vacuum rearrangement in massless electrodynamics, which results in the generation of a physical fermion mass, and the vacuum rearrangement concerned with the fall into the Coulomb centre with a large charge (Z > 137) is considered.     

Infrared problem and boson suppression in massless Abelian gauge theory

The vacuum polarization effects lead to a complete shielding of the charge and to a suppression of real boson excitations in massless Abelian gauge theory. Nevertheless, fermions interact by means of neutral vector currents. It is concluded that charged massless fermions cannot exist.     

Neutral Larkin-Ovchinnikov-Fulde-Ferrell state and chromomagnetic instability in two-flavor dense QCD

In two-flavor dense quark matter, we describe the dynamics in the single plane wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state satisfying the color and electric neutrality conditions. We find that because the neutral LOFF state itself suffers from a chromomagnetic instability in the whole region where it coexists with the (gapped or gapless) two-flavor superconducting phases, it cannot cure this instability in those phases. This is unlike the recently revealed gluonic phase which seems to be able to resolve this problem.     

Higher order symmetrizer and application to an unusual transport equation

We study a class of stationary transport equation with nonlocal low-order tems We obtain the existence and uniqueness of a solution in sobolev spaces     

求解复杂湍流的非线性涡黏性系数模型和代数应力模型

非线性涡黏性系数模型和代数应力模型联系了线性涡黏性系数湍流模型和完整的微分 雷诺应力模型.随着它们受到日益关注,其形式也越来越多样化.本篇综述的目的是对这些模 型加以总结并比较它们之间的共同点及不同之处,指出它们与完整微分雷诺应力模型之间的 关系,以及相对于线性涡黏性系数模型而言它们在预报流场上所具有的优势.