Phase space descriptions for simplicial 4D geometries
Phase space descriptions for simplicial 4D geometries
复制标题
单纯 4D 几何的相空间描述
DOI：
10.1088/0264-9381/28/6/065006
复制
发表时间：
2008
影响因子：
3.5
通讯作者：
J. Ryan
中科院分区：
文献类型：
--
作者：
B. Dittrich;J. Ryan
从离散的(4D)BF理论的正则相空间出发，我们实现了简单性约束的正则形式，并构造了单纯几何的相空间。我们的构造允许我们研究不同版本的Regge演算和使用连接变量的方法之间的联系，例如循环量子引力。我们发现，在固定的三角剖分下，与圈量子引力相关的(规范不变)相空间确实比长度甚至面积的Regge演算的相空间大。相反，它对应于[1]中定义的面积-角度Regge演算的相空间(在施加粘合约束之前，这确保了三角剖分的度量性)。最后，我们证明了对于三角剖分的一个子类，我们可以构造导致平坦4D时空的第一类哈密顿约束和微分同态约束。
Starting from the canonical phase space for discretized (4D) BF theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection between different versions of Regge calculus and approaches using connection variables, such as loop quantum gravity. We find that on a fixed triangulation the (gauge invariant) phase space associated with loop quantum gravity is genuinely larger than the one for length and even area Regge calculus. Rather, it corresponds to the phase space of area–angle Regge calculus, as defined in [1] (prior to the imposition of gluing constraints, which ensure the metricity of the triangulation). Finally, we show that for a subclass of triangulations one can construct first-class Hamiltonian and diffeomorphism constraints leading to flat 4D spacetimes.