论文标题
宇宙学旋转器
The Cosmological Spinor
论文作者
论文摘要
我们以前对Friedman-Lema \^ Itre-Robertson-Walker（FLRW）宇宙学的一维形式对称性进行了研究，并通过在经典层面上以经典级别的理论进行重新制定，以$ \ textrm {sl}（2，\ nathbbbb \ rant）$ - 新工具是宇宙学相位空间的规范转换，以旋转器的形式编写它，即在$ \ textrm {su}（1,1）（1,1）\ sim \ sim \ textrm {sl}的基本表示下转换的一对复杂变量。由此产生的FLRW Hamiltonian约束仅在旋转器中仅是二次的，而FLRW宇宙学被写为类似Schrödinger的动作原理。然后可以将共形转换写成适当的依赖时间$ \ textrm {sl}（2，\ mathbb {r}）$变换。我们以FLRW对任意二次汉密尔顿的可能的概括为结论，并讨论了旋转器作为重力的物质场或物质上的几何形状的解释。
We build upon previous investigation of the one-dimensional conformal symmetry of the Friedman-Lema\^ itre-Robertson-Walker (FLRW) cosmology of a free scalar field and make it explicit through a reformulation of the theory at the classical level in terms of a manifestly $\textrm{SL}(2,\mathbb{R})$-invariant action principle. The new tool is a canonical transformation of the cosmological phase space to write it in terms of a spinor, i.e. a pair of complex variables that transform under the fundamental representation of $\textrm{SU}(1,1)\sim\textrm{SL}(2,\mathbb{R})$. The resulting FLRW Hamiltonian constraint is simply quadratic in the spinor and FLRW cosmology is written as a Schrödinger-like action principle. Conformal transformations can then be written as proper-time dependent $\textrm{SL}(2,\mathbb{R})$ transformations. We conclude with possible generalizations of FLRW to arbitrary quadratic Hamiltonian and discuss the interpretation of the spinor as a gravitationally-dressed matter field or matter-dressed geometry observable.
