三维群场论中的威尔逊圈、几何算符和费米子
Wilson loops, geometric operators and fermions in 3d group field theory
摘要：
定义了群场论，其费曼图描述了具有变化的威尔逊圈观测量配置的三维引力和在每个顶点具有体积观测量的三维引力。体积观测量是由通常的自旋网络抓取算子创建的，这需要在群上引入矢量场。然后，我们用这个定义群场论，给出了一个先前定义的自旋泡沫模型耦合到引力的费米子场，和更简单的淬火近似，通过使用张量场的组。群场论自然包括微扰论每一阶费米子圈的总和。
英文摘要：
Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin network grasping operators which require the introduction of vector fields on the group. We then use this to define group field theories that give a previously defined spin foam model for fermion fields coupled to gravity, and the simpler quenched approximation, by using tensor fields on the group. The group field theory naturally includes the sum over fermionic loops at each order of the perturbation theory.
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