Dynamical Symmetry Breaking for Weinberg-Salam Model and Restoration at Finite Temperature

In this paper, we utilize Nambu-Jona-Lasinio (NJL) mechanism to discuss the dynamical symmetry breaking for Weinberg-Salam model. In the NJL mechanism the symmetry breaking not only is determined by the potential ofscalar field V(φ) but also has important relation with condensate of the fermion pair (φφ). We find that the coefficient of quadric term of scalar field μ² ≥ 0 can still cause symmetry breaking by virtue of (φφ) ≠ 0, and the vacuum expected value of scalar field obeys (φ) = (φφ), i.e., the order parameter which causes phase transition is the condensate of fermion pair (φφ). We also discuss the restoration problem of SU(2) × U(1) gauge symmetry breaking by the NJL mechanism at high temperatures.     

Dynamical Symmetry Breaking of Maximally Generalized Yang-Mills Model and Its Restoration at Finite Temperatures

In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Yang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.     

Dynamical Symmetry Breaking of Maximally Generalized Yang-Mills Model and Its Restoration at Finite Temperatures

In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Vang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.     

A Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry

A generalized Yang-Mills model, which contains, besides the vector part V_μ, also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of Nambu-Jona-Lasinio (NJL) mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills model. The combination of the generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.     

A Model with Spontaneous Symmetry Breaking and Its Kink Soliton Solution

A model with spontaneous symmetry breaking is presented. The exact kink which is stable and kink lattice solutions are obtained. When the parameter of the model λ tends to zero, all the results reduce to those of the well-known Φ⁴ model.     

Relativistic Hydrodynamics of Color-Flavor Locking Phase with Spontaneous Symmetry Breaking

We study the hydrodynamics of color-flavor locking phase of three flavors of light quarks in high density QCD with spontaneous symmetry breaking. The basic hydrodynamic equations are presented based on the Poisson bracket method and the Goldstone phonon and the thermo phonon are compared. The dissipative equations are constructed in the frame of the first-order theory and all the transport coefficients are also defined, which could be looked on as the general case including the Landau's theory and the Eckart's theory.     

A Model Study of Equation of State of QCD at Finite Chemical Potential and Zero Temperature

In this paper, we give a direct method for calculating the partition function, and hence the equation of state （EOS） of QCD at finite chemical potential and zero temperature. In the EOS derived in this paper the pressure density is the sum of two terms： the first term P（μ）｜μ=0 （the pressure density at μ = 0） is a μ-independent constant; the second term, which is totally determined by G[μ] （p） （the dressed quark propagator at finite μ）, contains all the nontrivial μ-dependence. By applying a general result in the rainbow-ladder approximation of the Dyson-Schwinger approach obtained in our previous study [Phys. Rev. C 71 （2005） 015205], G[μ]（p） is calculated from the meromorphic quark propagator proposed in [Phys. Rev. D 67 （2003） 054019]. From this the full analytic expression of the EOS of QCD at finite μ and zero T is obtained （apart from the constant term P（μ）｜μ=0, which can in principle be caJculated from the CJT effective action）. A comparison between our EOS and the cold, perturbative EOS of QCD of Fraga, Pisarski and Schaffner-Bielich is made. It is expected that our EOS can provide a possible new approach for the study of neutron stars.     

Maximally Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry

A maximally generalized Yang-Mills model, which contains, besides the vector part V_μ, also an axial-vector part A_μ, a scalar part S, a pseudoscalar part P, and a tensor part T_μν, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of the Nambu-Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the maximally generalized Yang-Mills model. The combination of the maximally generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.     

手征对称性动力学破缺和铜氧化物超导体相变的三维量子电动力学研究

利用三维量子电动力学理论中的Dyson-Schwinger方程方法, 研究了零温情况下平面铜氧化合物超导体的反铁磁相和d波超导相之间的相变. 通过在朗道规范下近似解析求解和数值求解完全耦合的Dyson-Schwinger方程、并将所得结果与1/N展开方法的结果相比较, 发现在半填充准费密子味道数约小于等于4的情况下, 通过手征对称性自发破缺, d波超导相可以演化到反铁磁相, 并且反铁磁相有可能与d波超导相共存. 通过进一步比较不同相的压强, 还说明反铁磁与d波超导共存相为稳定相, 从而反铁磁相确实可以与d波超导相共存.     

Spontaneous Symmetry Breaking of a Hyperbolic Sigma Model in Three Dimensions

Non-linear sigma models that arise from the supersymmetric approach to disordered electron systems contain a non-compact bosonic sector. We study the model with target space H², the two-hyperboloid with isometry group SU(1,1), and prove that in three dimensions moments of the fields are finite in the thermodynamic limit. Thus the non-compact symmetry SU(1,1) is spontaneously broken. The bound on moments is compatible with the presence of extended states.Dedicated to Freeman Dyson on the Occasion of his eightieth birthdayAcknowledgement T. Spencer would like to thank M. Disertori, K. Gawedzki, G. Papanicolau and S.R.S. Varadhan for helpful comments.     

The Effect of Spontaneous Breaking of Gauge Symmetry in Cosmology with Rotation

The effect of spontaneous breaking of gauge symmetry is studied for cosmological models with expansion and rotation with the Bianchi metrics of types II, IV, V, and VI. The conditions are defined wherein the effect is manifested in these models.     

Temperature Effects on the Equation of State and Symmetry Energy at Low and High Densities

Thermal properties of symmetric nuclear matter and pure neutron matter are studied in a selfconsistent Green’s function and Brueckner–Hartree–Fock approaches with the inclusion of the contact interaction using CDBONN potential. Also we investigate the temperature dependence of the symmetry energy. The symmetry energy at fixed density is found to generally decrease with temperature. The temperature effects on the nuclear matter symmetry energy are found to be stronger at lower densities while become much weaker at higher densities. The results of several microscopic approaches are compared. Also the results are compared with recent experimental data. There is good agreement between the experimental symmetry energy and those calculated in the Brueckner–Hartree–Fock approach.     

Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model

Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ-T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the Bose-Einstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.     

Calculation of Equation of State of QCD at Finite Chemical Potential and Temperature

In this paper, using path integral techniques we derive a model-independent formula for the pressure density P（μ, T） （or equivalently the partition function） of Quantum Chromodynamics （QCD）, which gives the equation of state （EOS） of QCD at finite chemical potential and temperature. In this formula the pressure density P（μ, T） consists of two terms： the first term （p（μ, T）｜T=0） is a μ-independent （but T-dependent） constant; the second term is totally determined by G[μ, T]（p, ωn） （the dressed quark propagator at finite μ and finite T）, which contains all the nontrivial μ-dependence. Then, in the framework of the rainbow-ladder approximation of the Dyson-Schwinger （DS） approach and under the approximation of neglecting the μ-dependence of the dressed gluon propagator, we show that G[μ, T]（p,ωn） can be obtained from G[T]（p,ωn ） （the dressed quark propagator at μ= 0） by the substitution ωn →ωn ＋ iμ. This result facilitates numerical calculations considerably. By this result, once C [T] （p, ωn） is known, one can determine the EOS of QCD under the above approximations （up to the additive term p（μ, T）｜T=0）. Finally, a comparison of the present EOS of QCD and the EOS obtained in the previous literatures in the framework of the rainbow-ladder approximation of the DS approach is given. It is found that the EOS given in the previous literatures does not satisfy the thermodynamic relation ρ（μ,T） =δp（μ,T）/δμ｜T.     

Dynamical Chiral Symmetry Breaking and Phase Transition of Cuprate Superconductors in QED3

With the coupled Dyson-Schwinger equations in the framework of the unified QED₃ theory, we study the phase transition between the antiferromagnet(AF) and the d-wave superconductor (dSC) of planar cuprates at T=0. By solving the coupled Dyson-Schwinger equations both analytically and numerically in rainbow approximation in Landau gauge and comparing the obtained results with that given in the 1/N expansion, we find that there exists a chiral symmetry breaking from dSC phase to AF phase when the quasi-fermion flavors N≤4 in half-filling and the AF phase can possibly coexist with the dSC phase in the underdoped region. By comparing the pressure between the coexistent AF-dSC phase and dSC phase, we find that AF-dSC coexisting phase is the stable phase, the AF phase can then coexist with the dSC phase.     

Electrical Neutrality and Symmetry Restoring Phase Transitions at High Density in a Two-Flavor Nambu-Jona-Lasinio Model

A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe twoflavor normal quark matter. Depending on whether mo/A, the ratio of dynamical quark mass in vacuum and the 3D momentum cutoff in the loop integrals, is less or greater than 0.413, the phase transition will be of the second or first order. A complete phase diagram of u quark chemical potential versus mo is given. With the electrical neutrality constraint, the region where the second order phase transition happens will be wider than the one without electrical neutrality limitation. The results also show that, for the value of m0/∧ from QCD phenomenology, the phase transition must be of the first order.     

Top-Quark Condensate at Finite Temperature and Electroweak Symmetry Restoration

The gap equation at finite temperature in the top-quark condensate scheme of electroweak symmetry breaking is proven to have the identical form in both the imaginary and real time formalisms of thermal field theory. By means of the gap equation, combined with the basic relation to define the vacuum expectation value v of the effective Higgs field, we analyze the dependence on temperature T and chemical potential p of the dynamical top-quark mass as the order parameter characteristic of symmetry breaking, and obtain the p-T criticality curve for symmetry restoration. We find out that the critical temperature T_c = 2υ for μ = 0 and the critical chemical potential μ_c = 2 π υ / √3 for T = 0. When μ = 0, the top-quark mass near T_c has the leading (T_c² - T²)^1/2 behavior with an extra factor dependent on temperature T and the momentum cutoff Λ. However, it is generally argued that the symmetry restoration at T ≥ T_c is still a second-order phase transition.     

Chiral Symmetry Breaking as a Phase Transition in QED Plus NJL Model

The chiral symmetry breaking (CSB) of massless &ED is studied analytically and then numerically by introducing a Nambu-Jona-Lasinio (NJL) term. We use the method of relativistic canonical transformation and random phase approximation to find the criterion for CSB (i.e., the condensation in vacuum) and the accompanying elementary excitations. The role played by NJL term, the scale anomaly and the meaning of critical point (α_c≈1.5) are discussed.     

Symmetry Breaking in Finite Volume-a Study in the O(N) Model

Spontaneous symmetry breaking plays a crucial role in quantum field theories and it occurs only for systems with infinite degrees of freedom. For a system in a large but finite volume, although the symmetry is not broken spontaneously, an adiabatic approximation can be applied to study the would-be broken symmetry. Lattice O(N) model is studied within the Hamiltonian approach. It is shown that the low-lying spectrum of the system can be explained using an adiabatic, or Born-Oppenheimer approximation, which turns out to become 1 an expansion in the inverse power of volume. In the infinite volume limit, the symmetry is broken while in the finite volume the slow rotation of the zero-momentum mode restores the symmetry and gives rise to the rotator spectrum, which has been observed in real Monte Carlo simulations.