标题： 施温格-凯尔迪什有效作用量用于具有近似对称性的流体力学 显示英文标题

标题： Schwinger-Keldysh effective action for hydrodynamics with approximate symmetries

摘要： 我们研究了最近在施温格-凯尔迪什（SK）路径上有效作用量方法发展的框架下具有近似对称性的流体力学理论。 我们采用虚假对称性变换的方法，针对小的显式对称破缺参数，系统地约束非平衡有效作用量中的对称破缺效应，该作用量描述了流体力学。 我们将这种方法应用于有限温度和密度下量子色动力学（QCD）中手征对称性的流体力学理论及其由夸克质量引起的显式破缺。 我们证明，虚假对称性和 Kubo-Martin-Schwinger (KMS) 关系决定了轴向对称性的 Ward-Takahashi 恒等式，即部分轴矢量电流守恒（PCAC）关系，其中包含一个与轴向化学势成正比的松弛项，其动力学系数至少是夸克质量的二阶项。 在手征对称性自发破缺且伪Nambu-Goldstone π介子作为流体力学变量出现的相中，这一松弛效应相对于 PCAC 关系中的常规 π 介子质量项是次主导的，后者是夸克质量的一阶项。 另一方面，在手征对称性恢复的相中，我们表明我们的松弛项，它是夸克质量的二阶项，成为轴电荷松弛的主要贡献。 因此，夸克质量在手征相变过程中主导的轴电荷松弛机制在参数上是不同的。 显示英文摘要

摘要： We study the hydrodynamic theories with approximate symmetries in the recently developed effective action approach on the Schwinger-Keldysh (SK) contour. We employ the method of spurious symmetry transformation for small explicit symmetry-breaking parameters to systematically constrain symmetry-breaking effects in the non-equilibrium effective action for hydrodynamics. We apply our method to the hydrodynamic theory of chiral symmetry in Quantum Chromodynamics (QCD) at finite temperature and density and its explicit breaking by quark masses. We show that the spurious symmetry and the Kubo-Martin-Schwinger (KMS) relation dictate that the Ward-Takahashi identity for the axial symmetry, i.e., the partial conservation of axial vector current (PCAC) relation, contains a relaxational term proportional to the axial chemical potential, whose kinetic coefficient is at least of the second order in the quark mass. In the phase where the chiral symmetry is spontaneously broken, and the pseudo-Nambu-Goldstone pions appear as hydrodynamic variables, this relaxation effect is subleading compared to the conventional pion mass term in the PCAC relation, which is of the first order in the quark mass. On the other hand, in the chiral symmetry-restored phase, we show that our relaxation term, which is of the second order in the quark mass, becomes the leading contribution to the axial charge relaxation. Therefore, the leading axial charge relaxation mechanism is parametrically different in the quark mass across a chiral phase transition.