核介质中强子性质的手征σ模型研究

采用手征σ模型描述核多体系统,考虑真空极化的影响,首先由核物质的饱和性质确定模型参数,进一步研究了强子性质在核介质中的变化。手征σ模型的研究结果给出,核子和ω介子的有效质量随核物质密度的增大而减小,但σ介子的有效质量随密度的增大而增大。这些结果与不满足手征对称性的Walecka模型结果进行了比较。计算中采用的重整化方法会对结果有一定的影响。The modification of hadron masses in nuclear medium is studied by using the chiral sigma model, which is extended to generate the omega meson mass by the sigma condensation in the vacuum in the same way as the nucleon mass. The chiral sigma model provides proper equilibrium properties of nuclear matter. It is shown that the effective masses of both nucleons and omega mesons decrease in nuclear medium, while the effective mass of sigma mesons increases at finite density in the chiral sigma model. The resuits obtained in the chiral sigma model are compared with those obtained in the Walecka model, which includes sigma and omega mesons in a non-chiral fashion.     

Nontopological finite temperature induced fermion number

We show that while the zero temperature induced fermion number in a chiral sigma model background depends only on the asymptotic values of the chiral field, at finite temperature the induced fermion number depends also on the detailed shape of the chiral background. We resum the leading low temperature terms to all orders in the derivative expansion, producing a simple result that can be interpreted physically as the different effect of the chiral background on virtual pairs of the Dirac sea and on the real particles of the thermal plasma. By contrast, for a kink background, not of sigma model form, the finite T induced fermion number is temperature dependent but topological.     

On gravitational dressing of 2D field theories in chiral gauge

After giving a pedagogical review of the chiral gauge approach to 2D gravity, with particular emphasis on the derivation of the gravitational Ward identities, we discuss in some detail the interpretation of matter correlation functions coupled to gravity in chiral gauge. We argue that in chiral gauge no explicit gravitational dressing factor, analogue to the Lionville exponential in conformal gauge, is necessary for left-right symmetric matter operators. In particular, we examine the gravitationally dressed four-point correlation function of products of left and right fermions. We solve the corresponding gravitational Ward identity exactly: in the presence of gravity this four-point function exhibits a logarithmic short-distance singularity, instead of the power-law singularity in the absence of gravity. This rather surprising effect is non-perturbative in the gravitational coupling and is a sign for logarithms in the gravitationally dressed operator product expansions. We also discuss some perturbative evidence that the chiral Gross-Neveu model may remain integrable when coupled to gravity.     

Dispersion Relation of σ Meson and Pion at Finite Nuclear Density in Chiral σ Model

The propagators of pion and sigma meson at a finite nuclear density and zero temperature are studied in chiral σ model. Their dispersion relations are calculated numerically in one-loop approximation. In order to avoid the so-called tachyon pole appearing in the one-loop propagators of pion and sigma meson, we regard the mass of sigma meson m_σ as a free parameter and adjust it to fit the nuclear saturation properties. For m_σ equal to 3075 MeV, the tachyon pole does not appear at the normal nuclear density. Thus the dispersion relation can be calculated in chiral σ model in one-loop level for the first time.     

Scalar Perturbations in Inflationary Models Based on the Non-Linear Sigma Model

The inflationary models based on the non-linear sigma model with the self-coupling potential are considered. The slow-roll solutions for long-wavelength inhomogeneities in general two-component chiral models and diagonal three-component chiral model of a special case are obtained. Scalar perturbations are calculated for two examples.     

η string formation in QCD chiral phase transition

In the paper we discuss the role of the axial U（1）A symmetry in the chiral phase transition using the U（Nf）R × U（Nf）L linear sigma model with two massless quark flavors. It is expected that above a certain temperature the axial U（1）A symmetry will be restored. A string-like static solution, the η string can be formed and detected in the ultrarelativistic heavy-ion collision process.     

The geodesic motion on generalized Taub-NUT gravitational instantons

A class of generalized Taub-NUT gravitational instantons is reported in five-dimensional Einstein gravity coupled to a non-linear sigma model. The geodesic dynamics of a spinless particle of unit mass on these static gravitational instantons is studied. This is accomplished by finding a generalized Runge-Lenz vector. Unlike the Kepler problem, or, the dynamics of a spinless particle on the familiar Taub-NUT gravitational instantons, the orbits are not conic sections.     

The Hierarchy Principle and the Large Mass Limit of the Linear Sigma Model

In perturbation theory we study the matching in four dimensions between the linear sigma model in the large mass limit and the renormalized nonlinear sigma model in the recently proposed flat connection formalism. We consider both the chiral limit and the strong coupling limit of the linear sigma model. Our formalism extends to Green functions with an arbitrary number of pion legs, at one loop level, on the basis of the hierarchy as an efficient unifying principle that governs both limits. While the chiral limit is straightforward, the matching in the strong coupling limit requires careful use of the normalization conditions of the linear theory, in order to exploit the functional equation and the complete set of local solutions of its linearized form.     

Gravitational collapse of colloidal gels

We present a unified framework for understanding the compaction of colloidal gels under their own weight. The dynamics of the collapse are determined by the value of the gravitational stress sigma(g), as compared to the yield stress sigma(Y) of the network. For sigma(g)sigma(Y), the network eventually yields, leading to rapid settling. In both cases, the rate of collapse is backflow limited, while its overall magnitude is determined by a balance between gravitational stress and network elastic stress.     

World-volume and target-space anomalies in the D = 10 super-fivebrane sigma model

The fields of the conjectured “heterotic” super-fivebrane sigma model in ten dimensions are made out of a well-known gravitational sector, the X and the ϑ, and of a still unknown heterotic sector which should be coupled to the Yang-Mills fields. We compute the one-loop d = 6 world-volume and D = 10 target-space Lorentz anomalies which arise from the gravitational sector of the heterotic super-fivebrane sigma model, using a method which we developed previously for the Green-Schwarz heterotic superstring. These anomalies turn out to carry an overall coefficient which is half of that required by the string-fivebrane duality conjecture. As a consequence, the world-volume anomaly vanishes if the heterotic fields consist of 16 (rather than 32) complex Weyl fermions on the world-volume. This implies that the string-fivebrane duality conjecture can not be based on a “heterotic” super-fivebrane sigma model with only fermions in the heterotic sector. Possible implications of this result are discussed.     

Quenched master field equations for unitary matrix models

We derive the quenched master field equations for constrained systems such as the O(N) non-linear sigma model, U(N)×U(N) chiral models, and U(N) lattice gauge theory. The master equations are algebraic, and involve quenching in both the space and “fifth” (Langevin) time directions. The quenched master field for the O(N) nonlinear sigma model is found exactly. The 0-dimensional unitary matrix model is solved perturbatively, and we recover the Gross-Witten result. The master equation for the U(N)×U(N) chiral model is set up for non-perturbative approximation methods, and some qualitative results are obtained.     

Mean-field approximation for the chiral soliton in a chiral phase transition

Using the mean-field approximation, we study the chiral soliton within the linear sigma model in a thermal vacuum. The chiral soliton equations with different boundary conditions are solved at finite temperatures and densities. The solitons are discussed before and after chiral restoration. We find that the system has soliton solutions even after chiral restoration, and that they are very different from those before chiral restoration, which indicates that the quarks are still bound after chiral restoration.     

Chiral self-gravitating cosmic vortices

In the framework of general relativity, an exact axisymmetric (vortex) solution of the equations of motion is obtained for the SU(2) symmetric sigma model. This solution is characterized by the topological charge (winding number) and angular deficit. In the linearized approximation, the Lyapunov stability of vortices is proved and the deflection angle of a light ray in the gravitational field of the vortex (gravitational lens effect) is calculated.     

Properties of the nucleon in the nuclear medium within a chiral quark-meson theory

The modifications of the nucleon structure due to the presence of an external baryon medium are investigated in a chiral quark meson theory. To that end the Nambu-Jona-Lasinio (NJL) model is combined with the projected chiral soliton model. The medium effects are incorporated using the medium modified values of the pion decay constant and the pion and sigma masses at finite density. These values are evaluated within the NJL model. Using functional integral techniques the latter is solved in a quark continuum at finite density. The effective meson values serve to fix the parameters of the linear chiral sigma model which is solved in a variational projected mean field approach in order to obtain the nucleon properties. All nucleon properties show modifications in the medium except for the pion nucleon coupling constant. The proton radius shows an increase of 19% and the nucleon mass a decrease of 17% if the medium reaches nuclear matter density. The magnetic moments and axial vector coupling constant are less modified. All form factors show remarkable reduction at finite transfer momenta.     

On the QCD phase structure from effective models

Some recent theoretical developments of the QCD phase diagram are summarized. Chiral symmetry restoration and the confinement/deconfinement transition at nonzero temperature and quark densities are analyzed in the framework of an effective linear sigma model with three light quark flavors. The sensitivity of the chiral transition as well as the existence of a critical end point in the phase diagram on the value of the sigma mass is explored. The influence of the axial anomaly on the chiral critical surface is addressed. Finally, the modifications by the inclusion of the Polyakov loop on the phase structure are investigated.     

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.     

A renormalization group analysis of leading logarithms in ChPT

We give strong evidence that the linear sigma model at small external momenta is an effective theory for the leading logarithms of chiral perturbation theory. Based on this evidence an attempt is made to sum the leading logarithms of chiral perturbation theory to all orders. We illustrate why this summation nonetheless fails when one uses standard renormalization group techniques of renormalizable quantum field theories.     

Goldberger-treiman relation in the renormalized sigma model

The regularization and renormalization of the full sigma model is worked out explicitly in the tree and one-loop approximation. Various renormalized quantities relevant for chiral symmetry breaking are listed. The numerically calculated Goldberger-Treiman relation is also compared with experiment.     

Dynamical formation of disoriented chiral condensates

We study the dynamical formation of disoriented chiral condensates in very high energy nucleus-nucleus collisions using Bjorken hydrodynamics and relativistic nucleation theory. It is the dynamics of the first order confinement phase transition which controls the evolution of the system. Every bubble or fluctuation of the new, hadronic, phase obtains its own chiral condensate with a probability determined by the Boltzmann weight of the finite temperature effective potential of the linear sigma model. We evaluate domain size and chiral angle distributions, which can be used as initial conditions for the solution of semiclassical field equations.