论文标题
同质迷你up型模型的动力对称性
Dynamical symmetries of homogeneous minisuperspace models
论文作者
论文摘要
我们研究了相对的相对对称性和均匀重力迷你up菜的保守电荷。这些（0+1） - 维度降低的一般相对性的降低是由时空指标定义的，在时空指标中，动态变量仅取决于时间坐标，并将其作为具有非平凡场空间公制（或超级计量）和有效电位的机械系统配方。我们展示了如何从野外空间度量的同一个杀伤向量中提取那些迷你up子空间的保守费用。在二维田间空间中，我们表现出$ \ mathfrak {sl}（2，2，\ mathbb {r}）\ oplus \ oplus \ mathbb {r} $的$ \ mathfrak {sl}（2，2，2，\ mathfrak {2，slfrak {2，slfrak {2，slfrak {2，slfrak {r} $）的通用8维对称代数。 $ \ mathfrak {h} _2 \ simeq \ mathbb {r}^4 $。我们将其应用于比安奇模型的同质宇宙学模型的系统研究。这扩展了$ \ Mathfrak {Sl}（2，\ Mathbb {r}）$代数的Friedmann-Lemaitre-Robertson-Walker宇宙学，以及Kantowski-Sachs Metrics描述黑洞室内的PoincaréSymmetry。在MinisuperSpace模型中已经存在这种丰富的对称结构，为量化和研究溶液生成机制的研究打开了新的大门。
We investigate the phase space symmetries and conserved charges of homogeneous gravitational minisuperspaces. These (0+1)-dimensional reductions of general relativity are defined by spacetime metrics in which the dynamical variables depend only on a time coordinate, and are formulated as mechanical systems with a non-trivial field space metric (or supermetric) and effective potential. We show how to extract conserved charges for those minisuperspaces from the homothetic Killing vectors of the field space metric. In the case of two-dimensional field spaces, we exhibit a universal 8-dimensional symmetry algebra given by the semi-direct sum of $\mathfrak{sl}(2,\mathbb{R})\oplus\mathbb{R}$ with the two-dimensional Heisenberg algebra $\mathfrak{h}_2\simeq\mathbb{R}^4$. We apply this to the systematic study of the Bianchi models for homogeneous cosmology. This extends previous results on the $\mathfrak{sl}(2,\mathbb{R})$ algebra for Friedmann-Lemaitre-Robertson-Walker cosmology, and the Poincaré symmetry for Kantowski-Sachs metrics describing the black hole interior. The presence of this rich symmetry structure already in minisuperspace models opens new doors towards quantization and the study of solution generating mechanisms.
