论文标题
部分可观测时空混沌系统的无模型预测
The BRST Double Complex for the Coupling of Gravity to Gauge Theories
论文作者
论文摘要
我们认为（有效的）量子相对论与标准模型（QGR-SM）耦合，并澄清graviton-ghosts是否与粒子有关。为此，我们检查了相应的BRST和反BRST对称性，这些对称性是由无穷小的差异和无穷小规变动产生的。特别是，我们研究了它们的特性和关系：我们发现所有差异都在相互抗衡，这意味着它们形成了双重复合物。特别是，我们将总BRST差异引入了差异和尺寸差异的总和，类似地将总抗Brst差异作为相应的反BRST差异的总和。 Furthermore, we identify the functionals in particle fields that are (co)cycles up to total derivatives with respect to the diffeomorphism differentials as scalar tensor densities of weight one: This implies that graviton-ghosts decouple from matter particles if and only if the Yang--Mills gauge fixing Lagrange density has said tensor density weight.此外，我们讨论了相关的量规固定费用：从De Donder和Lorenz量规固定条件开始，我们引入了一个总量规固定费用，从而生成了QGR-SM的完整量规固定和幽灵Lagrange密度。最后，我们表明，Brst Cocomplexes通过幽灵结合对相应的抗Brst络合物是同构的。值得注意的是，这将BRST共同体与它们各自的抗Brst同源性有关。
We consider (effective) Quantum General Relativity coupled to the Standard Model (QGR-SM) and clarify whether graviton-ghosts couple to matter particles. To this end, we examine the corresponding BRST and anti-BRST symmetries, which are generated by infinitesimal diffeomorphisms and infinitesimal gauge transformations. In particular, we study their properties and relations: We find that all differentials mutually anticommute, which implies that they form a double complex. In particular, we introduce the total BRST differential as the sum of the diffeomorphism and gauge BRST differentials and similarly the total anti-BRST differential as the sum of the respective anti-BRST differentials. Furthermore, we identify the functionals in particle fields that are (co)cycles up to total derivatives with respect to the diffeomorphism differentials as scalar tensor densities of weight one: This implies that graviton-ghosts decouple from matter particles if and only if the Yang--Mills gauge fixing Lagrange density has said tensor density weight. Moreover, we discuss the relevant gauge fixing fermions: Starting from the de Donder and Lorenz gauge fixing conditions, we introduce a total gauge fixing fermion that generates the complete gauge fixing and ghost Lagrange density of QGR-SM. Finally, we show that the BRST cocomplexes are isomorphic to their corresponding anti-BRST complexes via ghost conjugation. Notably, this relates the BRST cohomologies to their respective anti-BRST homologies.
