标题： $^3$氦-3宏观运动的外尔费米子的有效拉格朗日 显示英文标题

标题： Effective Lagrangian for the macroscopic motion of Weyl fermions in $^3$He-A

摘要： 我们考虑超流体$^3$He-A 的正常组分在Zubarev统计算符方法的框架内，在全局热力学平衡下的宏观运动。我们用泛函积分的语言表述相应的有效理论。对于由于时空相关的矩阵值 vierbein 引发的非平凡玻色背景中的超流体$^3$He-A 相中的涌现相对论费米子，我们明确计算了包含费米激发宏观运动的有效拉格朗日量，该 vierbein 具有非零挠率以及 Nieh-Yan 异常。我们不考虑超流体组分本身的动力学及其因正常组分宏观流动引起的反作用效应，而是将其视为外部背景，在其中正常组分的涌现相对论费米子移动。矩阵值 vierbein 的表述包含两个轴向带电 Weyl 费米子的额外二维内部自旋空间，这些费米子存在于费米点上，可以被一个具有实数值 vierbein、轴向阿贝尔规范场和混合狄拉克与内部自旋空间的自旋联络规范场所取代。我们详细地完成这种描述变化，并确定从全局热力学平衡下的 Zubarev 统计算符形式主义得出的超流体背景以及正常组分运动的约束条件。作为该理论的一个应用，我们考虑纯整数质量涡旋轴周围的宏观旋转。分析了正常组分对应的热力学量。我们的表述同时包含了超流体背景流和正常组分的宏观运动流，从而能够分析它们之间的相互关系。 显示英文摘要

摘要： We consider macroscopic motion of the normal component of superfluid $^3$He - A in global thermodynamic equilibrium within the context of the Zubarev statistical operator method. We formulate the corresponding effective theory in the language of the functional integral. The effective Lagrangian comprising macroscopic motion of fermionic excitations is calculated explicitly for the emergent relativistic fermions of the superfluid $^3$He - A phase immersed in a non-trivial bosonic background due to a space and time dependent matrix-valued vierbein featuring nonzero torsion as well as the Nieh-Yan anomaly. We do not consider the dynamics of the superfluid component itself and thereby its backreaction effects due to normal component macroscopic flow. It is being treated as an external background within which the emergent relativistic fermions of the normal component move. The matrix-valued vierbein formulation comprises an additional two dimensional internal spin space for the two axially charged Weyl fermions living at the Fermi points which may be replaced by one featuring a Dirac fermion doublet with a real valued vierbein, an axial Abelian gauge field and a spin connection gauge field mixing the Dirac and internal spin spaces. We carry out this change of description in detail and determine the constraints on the superfluid background as well as the the normal component motion as determined from the Zubarev statistical operator formalism in global thermodynamic equilibrium. As an application of the developed theory we consider macroscopic rotation around the axis of pure integer mass vortices. The corresponding thermodynamic quantities of the normal component are analyzed. Our formulation incorporates both superfluid background flow and macroscopic motion flow of the normal component and thereby enables an analysis of their interrelation.