论文标题
浆果阶段世界空间表示：轴向异常和经典动力学理论
Berry phase in the phase space worldline representation: the axial anomaly and classical kinetic theory
论文作者
论文摘要
在全球形式主义的相空间表示中，分析了浆果阶段的Weyl和Dirac Fermions。动力学理论都是在经典层面上构建的。尽管Weyl fermion案例在维度上降低，类似于量子力学中的理论，但狄拉克·费米昂（Dirac Fermion Case）以明显的Lorentz协变形式采用。为了实现非亚洲狄拉克·费米恩浆果阶段的经典动力学理论。还研究了轴向异常。已经发现，在绝热近似下，这对于促进经典动力学理论是必不可少的，无质量费米子的狄拉克操作员的索引消失了。即便如此，通过将藤川方法应用于Barut和Zanghi Spinors在全球范围内，轴向旋转与确切的非侧面浆果相变的相似性。
The Berry phase is analyzed for Weyl and Dirac fermions in a phase space representation of the worldline formalism. Kinetic theories are constructed for both at a classical level. Whereas the Weyl fermion case reduces in dimension, resembling a theory in quantum mechanics, the Dirac fermion case takes on a manifestly Lorentz covariant form. To achieve a classical kinetic theory for the non-Abelian Dirac fermion Berry phase a spinor construction of Barut and Zanghi is utilized. The axial anomaly is also studied at a quantum level. It is found that under an adiabatic approximation, which is necessary for facilitating a classical kinetic theory, the index of the Dirac operator for massless fermions vanishes. Even so, similarities of an axial rotation to an exact non-covariant Berry phase transform are drawn by application of the Fujikawa method to the Barut and Zanghi spinors on the worldline.
