自旋泡沫费米子：PCT对称性、狄拉克行列式和关联函数
Spinfoam Fermions: PCT Symmetry, Dirac Determinant, and Correlation Functions
摘要：
我们在自旋泡沫量子引力的框架下讨论费米子耦合。我们分析了引力-费米子自旋泡沫模型及其费米子关联函数。我们证明了自旋泡沫模型中的费米子场存在PCT对称性的自旋泡沫模拟，证明了自旋泡沫费米子关联函数的PCT定理。我们计算费米子狄拉克算符的行列式，其中狄拉克行列式的两种表示形式以图形展开的形式给出。我们计算的费米子关联函数，并表明，它们可以给出的自旋泡沫上的费曼图，其中的费曼传播子可以表示为一个离散的路径积分的世界线作用沿边缘的基础2-复杂。
英文摘要：
We discuss fermion coupling in the framework of spinfoam quantum gravity. We analyze the gravity-fermion spinfoam model and its fermion correlation functions. We show that there is a spinfoam analog of PCT symmetry for the fermion fields on spinfoam model, where a PCT theorem is proved for spinfoam fermion correlation functions. We compute the determinant of the Dirac operator for the fermions, where two presentations of the Dirac determinant are given in terms of diagram expansions. We compute the fermion correlation functions and show that they can be given by Feynman diagrams on the spinfoams, where the Feynman propagators can be represented by a discretized path integral of a world-line action along the edges of the underlying 2-complex.
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