用独立元格等效作用量研究三维U(1)格点规范理论的相结构

在格点规范理论中,应用变分累积展开方法,引入独立元格等效作用量,研究了三维U(1)格点规范理论的元格内能,得到连续的内能曲线,与Monte Carlo(MC)数据相符,表明理论是禁闭的.     

有限温度格点U(1)规范理论计算

用有限温度的变分-累积展开方法,计算了N_{τ=1的U(1)格点规范模型的序参量,结果与蒙特卡洛模拟符合,讨论了Nτ=1时出现的特殊简化,明确了变分条件定累积展开中所引入的参数和聚点法定参数的关系.}     

格点U(1)规范–Higgs(定模)模型的解析计算

用变分累积展开法,在格点上对基础表示的定模Hggs场与U(1)规范场的耦合系统的相结构进行了研究,变分参数用主值变分法辅之以聚点法来确定,得到了与Monte Carlo模拟很好符合的相图;并计算了N_τ=1的有限温度情形下定模U(1)-Higgs系统的Polyakov线〈L〉.     

有限温度U(1)格点规范模型的高阶累积展开之研究

在N3σ×N_τ(N_τ=1)的高温格点U(1)模型中,对序参数Polyakov线〈L〉作累积展开计算到五级近似.重点在于讨论累积展开在中间耦合区的行为,从累积展开与关联长度的联系阐明在中间耦合区高阶展开的必要性.采用n级展开对零级展开的修正为零的条件定n级计算中的变分参数,结果显示,不仅在强、弱耦合区,而且在中间耦合区(除了相变点附近)都与蒙特卡罗模拟有较好的符合,随着近似级别的增高,可信的计算可以越来越逼近相变点.这可能是变分累积展开方法作为近似解析方法的一大优点.     

包含六链方格的SU(2)改进作用量的累积展开变分研究

本文包含六链方格满足Symanzik要求的SU(2)格点规范作用量进行了累积展开变分研究,解析地计算了精确到二级累积展开的元格和六链方格的平均值,计算结果与Monte Carlo结果自洽.     

格点U(1)-Higgs系统的解析研究

运用变分累积展开方法研究变模荷为1的Higgs-U(1)耦合系统,给出了近似解析确定相变线的方法,得出d=4的相图与Monte Carlo定性符合,也给出了d=5的相图.     

SU(2)×SU(2)格点手征模型的进一步研究

本文利用变分─累积展开方法将SU(2)×SU(2)格点手征模型的自由能展开到第五级,分别用主值法和聚点法(accumulation point)确定变分参数,结果表明后者能得到与蒙特卡罗模拟更为一致的内能和比热曲线.     

独立元格试探作用量对3维SU(2)格点规范理论相结构的变分研究

应用独立元格试探作用量对3维SU(2)格点规范理论的相结构作了变分计算,所得内能曲线是光滑的,显示理论的禁闭性质.此计算改进了应用独立链试探作用量作变分累积展开方法所得的结果.     

U(1)规范理论的定量分析

在Migdal及Migdal-Kadanoff交换方案基础上导出了重整化群方程、并将其应用到Wilson形式的U(1)格点规范理论,给出了强耦合区,弱耦合区及临界耦合点,中间耦合区的数值结果.这些结果与严格的强耦合展开,弱耦合展开及Monte Carlo模拟结果一致.从而说明:本文得到的重整化群方程在讨论规范理论的非微扰特性方面是可行而有效的.     

有限温度格点SU(2)-Higgs系统的解析处理

有限温度格点规范理论的变分-累积展开处理推广到了格点SU(2)-Higgs系统Higgs场在基础表示的情况.通过计算Polyakov线至三级近似演示了方法,结果与蒙特卡罗计算的结果符合,并和平均场的计算结果作了比较.     

A minimalSU(2)×U(1)×U(1) electroweak model with mirror fermions

We present a minimal extension of the standard electroweak model, which accommodates mirror fermions, based onSU(2)×U(1)×U(1). Mirror mixing happens through sterile neutrino states and induces radiative mixing for charged leptons. Quarks and mirror quarks are not mixed with each other, consistent with the suppression of flavour changing neutral currents. Higgs sector, fermion masses and neutral currents are discussed. In this scheme there can be a secondZ boson as light as 0.2TeV.     

The Cabibbo angle in an SU(2) × U(1) × U(1) model

In the recently proposed SU(2) × U(1) × U(1) model the requirement that strangeness is naturally conserved in the natural Higgs couplings leads to tan θ_c ～m_dm_s.     

Neutral current phenomenology of supersymmetric SU(2) × U(1) × ≈U(1) models

The neutral current sector of a class of supersymmetric SU(2) × U(1) × ≈U(1) models is parametrized. Bounds on the neutral boson masses are obtained from the low energy data, and the implications of future experimental findings for these models are discussed.     

U(1)-invariant current forms

Let λ : U(1) → GL (V) be a linear representation. Lagrangians defined on J¹(T*M × V)whose universal current form is gauge invariant, are described in terms of gauge invariant Lagrangians and invariant functions on V. A characterization of gauge invariant Lagrangians depending on matter fields only, that is, L : J¹V → ?, is also obtained.     

Fermions as U(1) instantons

Anomalous quantization of the electromagnetic field allows non-trivial (anti) self-dual configurations to exist in four-dimensional Euclidian space-time. These instanton-like objects are described as massless spinor particles.      

The U(1) Higgs model

By using rigorous renormalization group methods we construct the continuum limit of the finite-volume lattice U(1) Higgs model in two and three dimensions. The method relies on a proof of the convergence of the effective action.Research supported in part by the National Science Foundation under grants PHY 82-03669 and PHY 81-17463