Kinetics of QCD phase transitions in effective models

在基本粒子的标准模型中，强相互作用是由量子色动力学（QCD）描述的，它是一种非阿贝尔规范理论，显示了渐近自由（即，有效耦合在具有大能量-动量转移的碰撞中变得微弱）和约束(即，基本成分，夸克和胶子，不能作为自由粒子被观察到，但被束缚在强子（介子作为一个夸克和一个反夸克的束缚态，重子作为三个夸克的束缚态）中，携带消失的净色电荷。因此，人们期望在具有强相互作用粒子的热而稠密的介质中，夸克和胶子在某种临界温度和/或密度下可以准自由地在该介质中运动。这意味着发生了一种相变，其中相关的自由度不再是强子，而是夸克和胶子（“部分子”）。这种物质状态被称为夸克-胶子等离子体（QGP）。除了基本的局部色规对称外，在轻夸克扇区（上、下、奇夸克）中，QCD还具有近似手性对称的特征，由于夸克凝聚体的形成，这种对称性在真空和低温、低密度条件下会自发地被打破。在高温下，人们预期这种夸克凝聚物会“融化”，从而恢复手性对称。从热平衡中的晶格- qcd计算可知，在高温和低净重子密度下，相变是连续的“交叉转变”，而有效强子模型表明，在高温和/或净重子密度下，相变是一级的。这进一步表明，这条一阶相变线在临界点处结束，在临界点处相变变为二阶。现在，人们希望找到这种一阶相变的特征，甚至是超相对论性重离子碰撞中的临界点。可能的特征是守恒量子数的波动，如净重子数，由相应统计分布的计算量量化。我们项目的主要目标是量子场理论研究，这种波动是否可以在有限寿命的有限系统中建立起来，就像重离子碰撞产生的“火球”一样。为此，我们希望在接近相变和临界点的非平衡状态下，利用相对论多体量子场理论（Schwinger-Keldysh形式主义）的实时公式，通过解析（通过推导适当的Kadanoff-Baym方程和相关的半经典输运方程）和计算机模拟来研究有效的量子场理论模型（如手性夸克-介子模型）。

Within the standard model of elementary particles the strong interaction is described by quantum chromodynamics (QCD), which is a non-Abelian gauge theory showing the fundamental properties of asymptotic freedom (i.e., the effective coupling becomes weak at collisions with large energy-momentum transfer) and confinement (i.e., the elementary constituents, the quark and gluons, cannot be observed as free particles but are bound in hadrons (mesons as bound states of a quark and an anti-quark and baryons as bound states of three quarks) that carry vanishing net-color charge.Thus, one expects that in a hot and dense medium of strongly interacting particles at some critical temperature and/or density the quarks and gluons can move quasi freely within that medium. This implies that a kind of phase transition occurs where the relevant degrees of freedom are not anymore hadrons but quarks and gluons ("partons"). This state of matter is called the quark-gluon plasma (QGP).In addition to the fundamental local color-gauge symmetry, in the light-quark sector (up, down, strange quarks) QCD is also characterized by an approximate chiral symmetry, which is spontaneously broken in the vacuum and at low temperatures and densities due to the formation of a quark condensate. At high temperatures one expects a "melting" of this quark condensate and thus the restoration of chiral symmetry.From lattice-QCD calculations in thermal equilibrium on knows that at high temperatures and low net-baryon densities the phase transitions are continuous "crossover transitions", while effective hadronic models suggest that at high temperatures and/or net-baryon densities the phase transition becomes of 1st order. This suggests further that this line of a first-order phase transition ends in a critical point, where the phase transition becomes of 2nd order.Now one hopes to find signatures of such first-order phase transitions or even a critical point in ultrarelativistic heavy-ion collisions. Possible signatures are fluctuations of conserved quantum numbers like the net-baryon number which are quantified by comulants of the corresponding statistical distributions. The main goal of our project is the quantum-field theoretical investigation whether such fluctuations can build up in a finite system of finite lifetime as the "fireballs" created in heavy-ion collisions. To that end we want to investigate effective quantum-field theoretical models (like the chiral quark-meson model) in nonequilibrium situations close to phase transitions and at the critical point, using the real-time formulation of relativistic many-body quantum-field theory (Schwinger-Keldysh formalism) both analytically (by deriving the appropriate Kadanoff-Baym equations and related semi-classical transport equations) and in computer simulations.