论文标题
共形量子重力分析
Analysis of Unitarity in Conformal Quantum Gravity
论文作者
论文摘要
我们通过协变运算符形式主义对Weyl的形式重力进行规范量化，并研究所得量子理论的单位性。通过引入辅助张量场将最初的第四阶理论简化为二阶衍生物，我们在BRST结构下确定了量子状态的完整量子空间，其中包括Faddeev-Popov幽灵场，与Weyl Transformations相对应。使用Kugo-Ojima四重奏机制，我们确定了量子状态的物理空间，并发现包含横向自旋-2态的子空间配备了一个不确定的内部产物度量标准和仅具有单个特定态的单粒子汉密尔顿。我们在此Spin-2子空间中为S-矩阵构建LSZ还原公式，并发现在散射事件中违反了单位性。这种违规发生的明确方式代表了关于量子重力二次理论的幽灵问题的新观点。
We perform a canonical quantization of Weyl's conformal gravity by means of the covariant operator formalism and investigate the unitarity of the resulting quantum theory. After reducing the originally fourth order theory to second order in time derivatives via the introduction of an auxiliary tensor field, we identify the full Fock space of quantum states under a BRST construction that includes Faddeev-Popov ghost fields corresponding to Weyl transformations. Using the Kugo-Ojima quartet mechanism, we identify the physical subspace of quantum states and find that the subspace containing the transverse spin-2 states comes equipped with an indefinite inner product metric and a one-particle Hamiltonian that possesses only a single eigenstate. We construct the LSZ reduction formula for the S-matrix in this spin-2 subspace and find that unitarity is violated in scattering events. The explicit way in which this violation occurs represents a new view on the ghost-problem in quadratic theories of quantum gravity.
