论文标题
循环量子重力和加倍问题的分辨率
Fermions in Loop Quantum Gravity and Resolution of Doubling Problem
论文作者
论文摘要
fermion繁殖物是从耦合到循环量子重力的fermion模型中详细得出的。作为繁殖器的成分，真空状态被定义为在背景几何形状下的某些有效的hamiltonian的基础状态，该几何形状类似于经典的Minkowski时空。此外，作为环量子重力的关键特征，使用图上的叠加来定义真空状态。事实证明，图叠加导致传播器是各种图上晶格场理论的传播器的平均值，因此在传播器中抑制了所有费米亚双打模式。这可以解决循环量子重力中的加倍问题。我们的结果表明，量子几何形状的叠加性质一方面应解决费米昂和基本离散性之间的张力，另一方面，与量子重力的连续限制有关。
The fermion propagator is derived in detail from the model of fermion coupled to loop quantum gravity. 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 loop quantum gravity, 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 loop quantum gravity. 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.
