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Assisted by multipartite entanglement, Quantum information may be split so that the original qubit can be reconstructed if and only if the recipients cooperate. This paper proposes an experimentally feasible scheme for splitting quantum information via W-type entangled states in cavity QED systems, where three-level Rydberg atoms interact with nonresonant cavities. Since W-type states are used as the quantum channel and the cavities are only virtually excited, the scheme is easy to implement and robust against decoherence, and the dependence on the quality factor of the cavities is greatly reduced.

By means of a formal expression of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by $A(p^2)\not{p}-B(p^2)$, we argue that, when temperature $T$ is less than the given infrared momentum cutoff $p_c$, $A(p^2)=1$ is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.

It is shown that, by means of canonical operator approach, the Ward-Takahashi identity (WTI) at finite temperature $T$ and finite chemical potential $\mu$ for complete vectorial vertex and complete fermion propagator can be simply proven, rigorously for Quantum Electrodynamics (QED) and approximately for Quantum Chromodynamics (QCD) where the ghost effect in the fermion sector is neglected. The WTI shown in the real-time thermal matrix form will give definite thermal constraints on the imaginary part of inverse complete Feynman propagator including self-energy for fermion and will play important role in relevant physical processes. When the above inverse propagator is assumed to be real, the thermal WTI will essentially be reduced to its form at $T=\mu=0$ thus one can use it in the latter's form. At this point, a practical example is indicated., Comment: 7 pages, Latex, no figure

High density phase transitions in a 4 dimensional Nambu-Jona-Lasinio model containing a single symmetry breaking order parameter coming from the fermion-antifermion condensates are researched and expounded by means of both the gap equation and the effective potential approach. The phase transitions are proven to be second order at a high temperature $T$; however at T=0, they are first- or second- order, depending on whether $\Lambda/m(0)$, the ratio of the momentum cutoff $\Lambda$ in the fermion loop integrals to the dynamical fermion mass $m(0)$ at zero temperature, is less than 3.387 or not. The former condition can not be satisfied in some models. The discussions further show complete effectiveness of the critical analysis based on the gap equation for second order phase transitions including determination of the condition of their occurrence., Comment: 8 pages, no figure

We have proven the general relations between the gap equations obeyed by dynamical fermion mass and the corresponding effective potentials at finite temperature and chemical potential in D-dimensional four-fermion interaction models. This gives an easy approach to get effective potentials directly from the gap equations. We find out explicit expressions for the effective potentials at zero temperature in the cases of D = 2, 3, and 4 for practical use.

Based on a general analysis of Green functions in the real-time thermal field theory, we have proven that the four-point amputated functions in a NJL model in the fermion bubble diagram approximation behave like usual two-point functions. We expound the thermal transformations of the matrix propagator for a scalar bound state in the $F\bar{F}$ basis and in the $RA$ basis. The resulting physical causal, advanced and retarded propagator are respectively identical to corresponding ones derived in the imaginary-time formalism and this shows once again complete equivalence of the two formalisms of thermal field theory on the discussed problem in the NJL model., Comment: 12 pages, Latex, no figues, published information of Ref.[12] has been added

We re-examine physical causal propagators for scalar and pseudoscalar bound states at finite temperature in a chiral NJL model, defined by four-point amputated functions subtracted through the gap equation, and prove that they are completely equivalent in the imaginary-time and real-time formalisms by separating carefully the imaginary part of the zero-temperature loop integral. It is shown that the same thermal transformation matrix of the matrix propagators for these bound states in the real-time formalism is precisely the one of the matrix propagator for an elementary scalar particle and this fact shows the similarity of thermodynamic property between a composite and elementary scalar particle. The retarded and advanced propagators for these bound states are also given explicitly from the imaginary-time formalism.

In a chiral UL(N) × UR(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 Tc, 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 UL(N) × UR(N) → UL+R(N) is valid and consistent with the real-time formalism of thermal field theory in this model.

We give the details of rigorous proof of some mass inequalitiee in a vector–like gauge theory based on any simple group . These mass inequalitiee lead to the conclusions that in such a theory the chiral symmetries associated with all representations of quarks must be spontaneously broken, and the persistent mass condition is justified for any composite particles when the vacuum angle is zero or massless quarks exist.

The analysis based on the renormalized effective potential indicates that, similar to in the 4D two-flavor Nambu-Jona-Lasinio (NJL) model, in a 2D two-flavor Gross-Neveu model, the interplay between the quark-antiquark and the diquark condensates in vacuum also depends on $G_S/H_S$, the ratio of the coupling constants in scalar quark-antiquark and scalar diquark channel. Only the pure quark-antiquark condensates exist if $G_S/H_S>2/3$ which is just the ratio of the color numbers of the quarks participating in the diquark and quark-antiquark condensates. The two condensates will coexist if $0, Comment: 6 pages, revtex4, no figure

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function $A(p^2)$ in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics (QCD), we obtain a calculable expression for the thermal effective potential which will be a useful means to research chiral phase transition in QCD in the real-time formalism., 5 pages, Latex, no figure

By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we have shown by explicit calculations that when T=0 the particle density will have a discontinuous jumping across the critical chemical potential $\mu_c$ in 2D and 3D Gross-Neveu (GN) model and these physically explain the first order feature of corresponding symmetry restoring phase transitions. For second order phase transitions in 3D GN model when $T\to 0$ and in 4D Nambu-Jona-Lasinio (NJL) model when T=0, it has been proven that the particle density itself will be continuous across $\mu_c$ but its derivative over the chemical potential $\mu$ will have a discontinuous jumping. The results give a physical explanation of implications of the tricritical point $(T,\mu)=(0,\mu_c)$ in 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions., Comment: 6 pages, no figure

Discrete symmetry breaking and possible restoration at finite temperature $T$ are analysed in 2D Gross-Neveu model by the real-time thermal field theory in the fermion bubble approximation. The dynamical fermion mass $m$ is proven to be scale-independent and this fact indicates the equivalence between the fermion bubble diagram approximation and the mean field approximation used in the auxialiary scalar field approach. Reproducing of the non-zero critical temperature $T_c=0.567 m(0)$, ($m(0)$ is the dynamical fermion mass at T=0), shows the equivalence between the real-time and the imaginary-time thermal field theory in this problem. However, in the real-time formalism, more results including absence of scalar bound state, the equation of criticality curve of chemical potential-temperature and the $\ln(T_c/T)$ behavior of $m^2$ at $T\stackrel{, Comment: 8 pages, Latex, no figures

The gap equation at finite temperature in the top-quark condensate scheme of electroweak symmetry breaking is proved to have the identical form in both the imaginary and the real time formalism 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 analyse the dependence on temperature T and chemical potential $\mu$ of the dynamical top-quark mass as the order parameter characteristic of symmetry breaking, and obtain the $\mu-T$ criticality curve for symmetry restoration. We find out that the critical temperature $T_{c}=2v$ for $\mu=0$ and the critical chemical potential $\mu_c=2\pi v/\sqrt{3}$ for T=0. When $\mu=0$, the top-quark mass near $T_c$ has the leading ${(T_c^2-T^2)}^{1/2}$ behavior with an extra factor dependent on temperature $T$ and the momentum cut-off $\Lambda$. However, it is generally argued that the symmetry restoration at $T\geq T_c$ is still a second-order phase transition., Comment: 12 pages, latex, 1 figure, Commun. Theor. Phys., to be published

A family gauge symmetry SUF(2) could emerge from a composite model of quarks and leptons under some assumptions of chiral hyperflavor symmetry-breaking pattern. Possible dynamical mechanisms which break the family and electroweak gauge group and produce quark-lepton masses are indicated and their phenomenologies are discussed qualitatively.

We analyze a class of SUSY composite models based on SU H ( N ), by using the asymptotic freedom constraint as well as the anomaly consistency condition. A semirealistic model with three families is found. We conjecture that a combination of the ordinary U A (1) and the U(1) associated to the R symmetry could be used to label the generations.

It is shown that the Z10 symmetry which survives the breaking of a combination of the axial UA(1) and the R symmetry in a susy composite model, can lead to the relation tg θ c ≅ (m d /m s ) 1 2 .

The observed quark mass hierarchy and the realistic mixing matrix of quark charged currents may be explained in a framework of a three-fermion composite model, if the quark masses are generated by the condensates of exotic colored fermions and in the dynamical mechanism, we incorporate the following conjecture that the four-preon hypercolor condensates, which are used to realize the spontaneous breaking of the family gauge group in the model, may correspond to two different mass scales. We also show that all the FCNC including the effective coupling in the model can be suppressed down to below the experimental limit.

The two possibilities (corresponding to various spontaneous breaking patterns for hyperflavor) for the color group SUC(3) factorized at the hypercolor scale ΛH for a kind of composite models are discussed, in which the color interaction is asymptotically non-free on the preon level, and it is pointed out that the two patterns could be distinguished experimentally by the great difference in number of the induced pseudogoldstones.

Constraints from the unification of non-gravitational interactions are discussed for a class of composite models of quarks and leptons with unbroken SU(N)H ⊗ SU(3)c ⊗ U(1)em interactions (H being hypercolor responsible for the binding of preons). Some new models are proposed in this connection. The minimal SU(7) unification is analyzed in detail for the case of N = 4.