论文标题
动态模糊光谱三元的BV量化
BV quantization of dynamical fuzzy spectral triples
论文作者
论文摘要
本文提供了一项系统的研究，该研究对Barrett和合作者提出的量子重力的动力模糊光谱三重模型进行了系统研究。我们为这些模型开发了经典和扰动的量子BV形式，这特别是导致扰动量子相关函数的明确同源结构。我们表明，幽灵和防field对此类相关功能的贡献的相关性在很大程度上取决于dirac运算符$ d_0 $ aboutb的背景，尤其是它破裂的规格对称性数量。这将通过研究量子扰动左右来说明。
This paper provides a systematic study of gauge symmetries in the dynamical fuzzy spectral triple models for quantum gravity that have been proposed by Barrett and collaborators. We develop both the classical and the perturbative quantum BV formalism for these models, which in particular leads to an explicit homological construction of the perturbative quantum correlation functions. We show that the relevance of ghost and antifield contributions to such correlation functions depends strongly on the background Dirac operator $D_0$ around which one perturbs, and in particular on the amount of gauge symmetry that it breaks. This will be illustrated by studying quantum perturbations around 1.) the gauge-invariant zero Dirac operator $D_0=0$ in a general $(p,q)$-model, and 2.) a simple example of a non-trivial $D_0$ in the quartic $(0,1)$-model.
