Influence of Finite Chemical Potential on Critical Boson Mass in QED3

Using the coupled Dyson-Schwinger equation for the fermion propagator at finite chemical potential μ, we investigate the fermion chiral condensate when the gauge boson mass is nonzero in QED3. We show that the chiral symmetry restores when the boson mass is large enough, and the critical boson mass depends little on μ.     

Dual fermion condensate and phase transition in QED3

In this paper,we investigate the behaviors of dual fermion condensate in QED 3 under variation of temperature.By means of Dyson-Schwinger equation for the fermion propagator,we extract the dual fermion condensate and compare its behavior with the ordinary chiral fermion condensate and the chiral susceptibility.It is found that the dual fermion condensate cannot be regarded as the order parameter for the confinement-deconfinement phase transition in QED 3.Furthermore,the change of the dual fermion condensate around the chiral phase transition point observed in the present work must therefore be interpreted as solely induced by the chiral transition.     

Calculation of Particle-Number Susceptibility of QED3 at Finite Temperature

Based on the external field approach and the differential form of Ward identity, we derive a more compact formula for the particle-number susceptibility in QED3 at finite temperature. Using the zero frequency approximation the numerical value of the particle-number susceptibility is calculated in the Dyson-Schwinger approach for the case that the number of fermion flavours equals one and two, respectively. An enhanced fluctuation of the particlenumber density is observed across the transition temperature, which should be an essential characteristic of chiral phase transition in QED3.     

Spontaneous chiral-symmetry breaking of lattice QCD with massless dynamical quarks

One of the most challenging issues in QCD is the investigation of spontaneous chiral-symmetry breaking, which is characterized by the non-vanishing chiral condensate when the bare fermion mass is zero. In standard methods of the lattice gauge theory, one has to perform expensive simulations at multiple bare quark masses, and employ some modeled functions to extrapolate the data to the chiral limit. This paper applies the probability distribution function method to computing the chiral condensate in lattice QCD with massless dynamical quarks, without any ambiguous mass extrapolation. The results for staggered quarks indicate that this might be a promising and efficient method for investigating the spontaneous chiral-symmetry breaking in lattice QCD, which deserves further investigation.     

Temperature dependence of quarks and gluon vacuum condensate in the Dyson-Schwinger Equations at finite temperature

Based on the Dyson-Schwinger Equations (DSEs), the two-quark vacuum condensate, the four-quark vacuum condensate, and the quark gluon mixed vacuum condensate in the non-perturbative QCD vacuum state are investigated by solving the DSEs with rainbow truncation at zero- and finite-temperature, respectively. These condensates are important input parameters in QCD sum rule with zero and finite temperature, and in studying hadron physics, as well as predicting the quark mean squared momentum m₀²-also called quark virtuality in the QCD vacuum state. The present calculated results show that these physical quantities are almost independent of the temperature below the critical point temperature T_c=131 MeV, and above T_c the chiral symmetry is restored. For comparison we calculate the temperature dependence of the "in-hadron condensate" for pion. At the same time, we also calculate the ratio of the quark gluon mixed vacuum condensate to the two-quark vacuum condensate by using these condensates, and the unknown quark mean squared momentum in the QCD vacuum state has been obtained. The results show that the ratio m₀²(T) is almost flat in the temperature region from 0 to T_c, although there are drastic changes of the quark vacuum condensate and the quark gluon mixed vacuum condensate at the region. Our predicted ratio comes out to be m₀²(T)=2.41 GeV² at the Chiral limit, which is consistent with other theory model predictions, and strongly indicates the significance that the quark gluon mixed vacuum condensate has played in the virtuality calculations.     

带Wilson费米子的格点Schwinger模型中〈ψψ〉的变分研究

本文用变分方法计算带Wilson费米子的格点Schwinger模型中的手征对称破缺的序参数〈ψψ〉,得到较好的结果.     

三维QED中的几个重要问题（英文）

三维量子电动力学是一种看上去比较简单的Abel 类型的非微扰系统,其本身却有很多需要澄清的基本问题。从该系统是否具有密度依赖性,有限温下是否具有动力学自发对称破却以及规范玻色子可否具有质量这三方面出发,阐述了对三维量子电动力学一些基本问题的看法。Quantum electrodynamics in (2+1) dimensions (QED₃) is an important nonperturbative system. This seems relatively simple Abel system, there are several issues that need to be clarified: whether or not the partition function of the system depends on chemical potential; whether or not there exists dynamical chiral symmetric breaking; whether or not the boson can acquires nonzero mass. In this paper, we give an in sight of the traits of QED₃ from the dependence of density, temperature and massive boson to discuss those problems.     

QCD类规范的南部模型中费米子与动力学产生的介子的密度效应

将两味(N_f=2)情况下的QCD类规范的南部模型应用到核物质中并得到了费米子的能隙方程.与四费米子相互作用部分相比,胶子部分对费米子质量约有1/4的贡献.手征序参量与QCD求和规则所预言的结果符合得很好.基于能隙方程,得到了标量与赝标量介子的一系列动力学性质,理论结果很好地符合了实验.     

Curvature of Pseudocritical Transition Line for Two-Flavor QCD with Improved Kogut-Susskind Quarks

The results on the curvature of a pseudocritical transition line for two-flavor QCD through lattice simulations are presented. The simulations are carried out with Symanzik-improved gauge action and Asqtad fermion action on a lattice 12~3×4 at quark mass am = 0.010. At the imaginary chemical potentials aμ_I = 0.050, 0.150, 0.200,0.225 and 0.250, we investigate the chiral condensate φφ, plaquette variable P and imaginary part of Polyakov loop Im(L) and their susceptibilities. Analytic continuation from an imaginary chemical potential to a real one is used to obtain the expression for transition temperature as a function of the chemical potential. The eurvature is 0.0326(46).     

(2+1)维SU(2)四费米子耦合理论的Ward-Takahashi恒等式和质量谱

本文利用含复合场的Ward-Takahashi恒等式研究了(2+1)维SU(2)四费米子耦合的理论.在SU(2)手征对称性既有明显破缺又有动力学破缺时,得到了动力学所生成的费米子质量和束缚态的谱性质,并讨论了矢量流和轴矢流的性质.结果表明:束缚态π_α获得了质量并得到轴矢流部分守恒的结论;当费米子的流质量较小时,Goldberger-Treiman关系近似成立.     

Effect of Fermion Velocity on Phase Structure of QED3

Dynamical chiral symmetry breaking (DCSB) in thermal QED₃ with fermion velocity is studied in the framework of Dyson-Schwinger equations. By adopting instantaneous approximation and neglecting the transverse component of gauge boson propagator at finite temperature, we numerically solve the fermion self-energy equation in the rainbow approximation. It is found that both DCSB and fermion chiral condensate are suppressed by fermion velocity. Moreover, the critical temperature decreases as fermion velocity increases.     

Critical Number of Fermion Flavors at Finite Chemical Potential in QED3

We propose a new method for calculating the dressed fermion propagator at finite chemical potential in QED3 under the rainbow approximation of Dyson-Schwinger equation. In the above approximation, we show that the dressed fermion propagator at finite chemical potential # has the form S（p） = iγ.p^-A（p^-2） ＋ B（ p^-2） with p^-μ= （p^-1p3 ＋ iμ）. Using this form of fermion propagator at nonzero chemical potential, we investigate the Dyson-Schwinger equation for the dressed fermion propagator at finite chemical potential and study the effects of the chemical potential on the critical number of the fermion flavors.     

Behavior of Vacuum Polarization of Gauge-Boson and Wavefunction Renormalization Factor of Fermion in Different Phases of QED3

We investigate the behavior of the vacuum polarization of the gauge-boson Π and the wave-function renormalization factor of the fermion A in QED₃, using the coupled Dyson-Schwinger equations for the gauge-boson and fermion propagator. Using several different ansätze for the fermion-gauge-boson vertex, we find that the wave-function renormalization factor A and especially the vacuum polarization Π have different behaviors in the dynamical chiral symmetry breaking phase and in the chiral symmetric phase and hence in the phenomenological applications of QED₃ one should choose different forms of gauge-boson propagator for these two phases. We also find that when adopting a specific ansätze of the fermion-gauge-boson vertex (ansätze (3)) the vacuum polarization function equals its one-loop perturbative result in the chiral symmetric phase. This fact suggests that in QED₃ the Wigner vacuum corresponds to the perturbative vacuum.     

Supersymmetry for Fermion Masses

It is proposed that supersymmetry （SUSY） may be used to understand fermion mass hierarchies. A family symmetry ZSL is introduced, which is the cyclic symmetry among the three generation SU（2） doublets. SUSY breaks at a high energy scale - 10^11 GeV. The electroweak energy scale- 100 GeV is unnaturally small No additional global symmetry, like the R-parlty, is imposed. The Yukawa couplings and R-parity violating couplings all take their natural values, which are О（10^0 -10^-2）. Under the family symmetry, only the third generation charged ferrnions get their masses. This family symmetry is broken in the soft SUSY breaking terms, which result in a hierarchical pattern of the fermion masses. It turns out that for the charged leptons, the r mass is from the Higgs vacuum expectation value （VEV） and the sneutrino VEVs, the muon mass is due to the sneutrino VEVs, and the electron gains its mass due to both ZZL and SUSY hreaking. The large neutrino mixing are produced with neutralinos playing the partial role of right-handed neutrinos. │Ve3│, which is for Ve-Vr mixing, is expected to be about 0.1. For the quarks, the third generation masses are from the Higgs VEVs, the second generation masses are from quantum corrections, and the down quark mass due to the sneutrino VEVs. It explains me/ms, ms/me, md 〉 mu and so on. Other aspects of the model are discussed.     

Fermion Coherent State Studies of One-Dimensional Hubbard Model

We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as ｜〉=[f＋∑^tφk1σ1hk2σ2ck3σ3hk4σ4 ∏exp（ρck1σ1 hk2σ2）]｜〉0,where φ and ρ are the coupling constants. Our results are then compared to those of varlational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto-Carlo method （VMC） as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.     

UL(N) x UR(N)-Invariant Four-Fermion Interactions and Nambu-Goldstone Mechanism at Finite Temperature

In a chiral U_L(N) x U_R(N) fermion model of NJL-form, we prove that, if all the fermions are assumed to have equal masses and equal chemical potentials, then at the finite temperature T below the symmetry restoration temperature T_c, there will be N² massive scalar composite particles and N² massless pseudoscalar composite particles (Nambu-Goldstone bosons). This shows that the Goldstone theorem at finite temperature for spontaneous symmetry breaking U_L(N) x U_R(N) → U_L+R(N) is valid and consistent with the real-time formalism of thermal field theory in this model.     

Fermion Self-Energy and Chiral Symmetry Breaking from Four-Fermion and Gauge Interactions

The exact analytic solutions of the linearized Schwinger-Dyson equation of fermion self-energy are used to obtain the effective four-fermion and gauge coupling criticality curves for dynamical chiral symmetry breaking. The results show that when the zero-momentum gauge coupling a(0) < a₀(0), the critical gauge coupling in the pure gauge interaction case, the minimal critical four-fermion coupling β_min is always nonzero and positive and will go up as the a(0) decreases. The use of the exact solutions also allows us to make quite definite estimations of the momentum scales where chiral symmetry breaking would happen if the values of an infrared parameter ξ are given separately.     

Running flavor number and asymptotic freedom in the normal phase of QED

In the normal phase (where no dynamical fermion mass generation occurs) of the D-dimensional quantum electrodynamics with N_f flavors of fermions, we derive an integral equation which should be satisfied by (the inverse of) the wave function renormalization of the fermion in the Landau gauge. For this we use the inverse Landau-Khalatnikov transformation connecting the nonlocal gauge with the Landau gauge. This leads to a similar equation for the running flavor number in the framework of the 1/N_f resumed Schwinger-Dyson equation. Solving the equation analytically and numerically, we study the infrared behavior and the critical exponent of the 3-dimensional QED (QED₃). This confirms that the flavor number in QED₃ runs according to the β function which is consistent with the asymptotic freedom as that in 4-dimensional QCD.     

A Model of Fermion Masses and Flavor Mixings with Family SymmetrySU(3)\otimes U(1)

The family symmetrySU}(3)\otimes U(1) is proposed to solve flavor problems about fermion masses and flavor mixings. It is breaking is implemented by some flavon fields at the high-energy scale. In addition a discrete group Z₂ is introduced to generate tiny neutrino masses, which is broken by a real singlet
scalar field at the middle-energy scale. The low-energy effective theory is elegantly obtained after all of super-heavy fermions are integrated out and decoupling. All the fermion mass matrices are regularly characterized by four fundamental matrices and thirteen parameters. The model can perfectly fit and account for all the current experimental data about the fermion masses and flavor mixings, in particular, it finely predicts the first generation
quark masses and the values ofθ₁₃^l and J_CP^l in neutrino physics. All of the results are promising to be tested in the future experiments.