论文标题
重力迷你 - 苏普斯空间中的schrödinger对称性
Schrödinger Symmetry in Gravitational Mini-Superspaces
论文作者
论文摘要
我们证明，在Schrödinger组下，描述宇宙学和黑洞力学的最简单引力对称性还原模型是不变的。我们考虑了装有无质量标量场和Schwarzschild黑洞力学的扁平FRW宇宙学，使用Eisenhart-Duval（ED）升力法构建其保守的电荷，并表明它们形成了Schrödinger代数。我们的方法说明了如何分析田间空间几何形状的ED升力和更标准的方法在揭示这些系统的不同对称性集合中的互补性。我们进一步确定了这两种模型的无限二维对称性，该模型是由在Witt代数的两个副本中组织的保守电荷产生的。这些扩展的电荷代数提供了这些均质引力部门的新代数表征。他们指导其量化的路径，并开辟了通往量子宇宙学和量子黑洞模型非线性扩展的道路，该模型就田间空间中的流体动力方程式而言。
We prove that the simplest gravitational symmetry reduced models describing cosmology and black holes mechanics are invariant under the Schrödinger group. We consider the flat FRW cosmology filled with a massless scalar field and the Schwarzschild black hole mechanics, construct their conserved charges using the Eisenhart-Duval (ED) lift method and show that they form a Schrödinger algebra. Our method illustrates how the ED lift and the more standard approach analyzing the geometry of the field space are complementarity in revealing different set of symmetries of these systems. We further identify an infinite-dimensional symmetry for those two models, generated by conserved charges organized in two copies of a Witt algebra. These extended charge algebras provide a new algebraic characterization of these homogeneous gravitational sectors. They guide the path to their quantization and open the road to non-linear extensions of quantum cosmology and quantum black holes models in terms of hydrodynamic equations in field space.
