当前研究量子色动力学的非微扰性质的一个重要方向是研究高密度下的强相互作用系统。高密度的致密星为该研究提供了天然的'实验室'。Dyson-Schwinger方程方法具有很好的量子色动力学理论基础，是研究该问题的非常好的理论方法。本项目拟采用Dyson-Schwinger方程方法研究高密度夸克物质的状态方程并应用于计算致密星的性质。基于我们已有的工作并结合Dyson-Schwinger方程方法在研究真空强子性质方面的最新进展，我们拟改进有限化学势下的夸克-胶子顶点与胶子传播子模型，在此基础上得到更为合理的夸克物质状态方程。然后，采用得到的高密夸克物质状态方程计算中子星内的强子-夸克相变和混杂星的结构，使混杂星性质更符合观测的限制。这一项目的研究有助于加深对非微扰量子色动力学的认识，并为研究高密度夸克物质和致密星性质提供好的理论基础。

Strong interacting system at high densities is a hot topic in study of non-perturbative quantum chromdynamics (QCD). Compact stars provide natural "laboratories" for such study. Dyson-Schwinger equations (DSE) approach is well based on QCD, and provides a good theoretical framework for studying dense quark matter. This proposal is to investigate the equation of state (EoS) of quark matter at high densities in the framework of DSE, and apply it to study of compact stars. Based on our previous work and recent developments on study of hadron properties with DSE approach, we plan to improve the model of quark-gluon vertex and gluon propagator at finite chemical potentials, and try to obtain a more realistic EoS of dense quark matter. Then, we will compute the hadron-quark phase transition in the interior of neutron stars and the structure of hybrid stars by using the EoS mentioned above, so that it is possible to obtain a good agreement between our theoretical results and observations of compact stars. This study is helpful for understanding non-perturbative QCD, and provides theory foundations for investigation of dense quark matter and compact stars.