Fermions in loop quantum gravity and resolution of doubling problem
Fermions in loop quantum gravity and resolution of doubling problem
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DOI：
10.1088/1361-6382/acf26b
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发表时间：
2022-12
影响因子：
3.5
通讯作者：
Cong Zhang;Hongguang Liu;Muxin Han
中科院分区：
文献类型：
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作者：
Cong Zhang;Hongguang Liu;Muxin Han
从费米子与圈量子引力耦合模型出发，详细推导了费米子传播子。作为传播子的一个组成部分，真空态被定义为在类似于经典闵可夫斯基时空的相干态给出的背景几何下某些有效费米子汉密尔顿量的基态。此外，作为LQG的一个重要特征，图上的叠加被用来定义真空态。事实证明，图形叠加导致传播子是在各种图形上的格点场理论的传播子的平均值，使得所有的费米子倍频模在传播子中被抑制。这解决了LQG中的加倍问题。结果表明，量子几何的叠加性质一方面解决了费米子与基本离散性之间的矛盾，另一方面又与量子引力的连续极限有关。
The fermion propagator is derived in detail from the model of fermion coupled to loop quantum gravity (LQG). As an ingredient of the propagator, the vacuum state is defined as the ground state of some effective fermion Hamiltonian under the background geometry given by a coherent state resembling the classical Minkowski spacetime. Moreover, as a critical feature of LQG, the superposition over graphs is employed to define the vacuum state. It turns out that the graph superposition leads to the propagator being the average of the propagators of the lattice field theory over various graphs so that all fermion doubler modes are suppressed in the propagator. This resolves the doubling problem in LQG. Our result suggests that the superposition nature of quantum geometry should, on the one hand, resolve the tension between fermion and the fundamental discreteness and, on the other hand, relate to the continuum limit of quantum gravity.