论文标题
dyson-schwinger方程中Gluon和Ghost Expagor的温度依赖性
Temperature Dependence of Gluon and Ghost Propagators in a Dyson-Schwinger Equations context
论文作者
论文摘要
我们根据Landau仪表中的彩虹截断的Dyson-Schinginger方程，研究了鬼魂和Gluon传播器的有限温度结构。该方法用于对真空的夸克，幽灵和gluon繁殖物进行建模，以扩展到有限的温度。在欧几里得空间中，在Matsubara假想时间的形式主义中，有必要将横向和纵向区分，相对于热浴，Gluon敷料功能，为此，Dyson-Schwinger方程将其分为相应的耦合方程系统。该系统在彩虹近似中被认为是有限温度并以数值求解的。 Ghost和Gluon传播器的解决方案是作为温度$ t $，Matsubara频率$ω_n$和三型摩托马平方$ {\ bf k}^2 $的函数获得的。发现，对于零Matsubara频率，幽灵和Gluon敷料的依赖性在$ {\ bf k}^2 $上对温度$ t $不敏感，而在$ {\ bf k}^2 = 0 $下，他们对$ t $的依赖性很强。还研究了对Matsubara频率$ω_n$的依赖性。对Dyson-Schwinger方程的解决方案进行的数值分析表明，在温度的某些值$ T_0 \ SIM 150 $ MEV的某些值下，迭代过程不会更长的时间收敛。在$ T_0 $附近，纵向Gluon繁殖物的增加非常迅速，而横向传播器则表现出任何不规则性。这与在此温度间隔内在QCD晶格计算中获得的结果的定性一致。
We investigate the finite-temperature structure of ghost and gluon propagators within an approach based on the rainbow truncated Dyson-Schwinger equations in Landau gauge. The method, early used for modeling the quark, ghost and gluon propagators in vacuum, is extended to finite temperatures. In Euclidean space, within the Matsubara imaginary-time formalism it is necessary to distinguish between the transversal and longitudinal, with respect to the heat bath, gluon dressing functions, for which the Dyson-Schwinger equation splits into a corresponding system of coupled equations. This system is considered within the rainbow approximation generalized to finite temperatures and solved numerically. The solutions for the ghost and gluon propagators are obtained as functions of temperature $T$, Matsubara frequency $Ω_n$ and three-momentum squared ${\bf k}^2$. It is found that, for zero Matsubara frequency, the dependence of the ghost and gluon dressing functions on ${\bf k}^2$ are not sensitive to the temperature $T$, while at ${\bf k}^2=0$ their dependence on $T$ is quite strong. Dependence on the Matsubara frequency $Ω_n$ is investigated as well.The performed numerical analysis of the solution of the Dyson-Schwinger equations shows that at certain value of the temperature $T_0\sim 150$ MeV the iteration procedure does not longer converge. In the vicinity of $T_0$ the longitudinal gluon propagator increases quite fastly, whereas the transversal propagator does not exhibit any irregularity. This in a qualitative agreement with results obtained within the QCD lattice calculations in this temperature interval.
