标题： Weyl费米子在$^3$He-A中宏观运动的有效拉格朗日量 显示英文标题

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

摘要： 我们考虑在Zubarev统计算子方法的框架下，宏观运动的$^3$He-A处于全局热力学平衡状态。 我们用泛函积分的语言表述相应的有效理论。 计算了包含费米激发宏观运动的有效拉格朗日量，该拉格朗日量针对超流体$^3$He-A相中出现的相对论性费米子，在由于具有非零挠率以及Nieh-Yan反常的空间和时间依赖矩阵值四维标架所引起的非平凡玻色背景下的情况进行了明确计算。 矩阵值四维标架表述包含了一个额外的二维内部自旋空间，该空间可以被一个具有实值四维标架、两个阿贝尔规范场以及混合狄拉克自旋空间和内部自旋空间的费米理论所替代。 作为该理论的应用，我们考虑纯整数质量涡旋轴周围的宏观旋转。 分析了正常组分的相应热力学量。 显示英文摘要

摘要： We consider macroscopic motion of $^3$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 in the non-trivial bosonic background due to a space and time dependent matrix-valued vierbein featuring nonzero torsion as well as the Nieh-Yan anomaly. The matrix-valued vierbein formulation comprises an additional two dimensional internal spin space which may be replaced by one featuring a fermionic theory with a real valued vierbein, two Abelian gauge fields and a spin connection mixing the Dirac and internal spin spaces. As an application of the developed theory we consider macroscopic rotation around the axis of the pure integer mass vortices. The corresponding thermodynamical quantities of the normal component are analysed.