哈密顿引力的自发破缺Lorentz对称
Spontaneously broken Lorentz symmetry for Hamiltonian gravity
摘要：
在阿施特卡的广义相对论的哈密顿公式中，以及在圈量子引力中，洛伦兹协变性是一个微妙的问题，一直受到强烈的争论。维持明显的洛伦兹协方差似乎需要引入复值场，这对量子化构成了重大障碍，或者需要引入额外的（通常是第二类）约束，其解决方案使得所得到的相空间变量更难在时空图像中解释。在回顾了困难的来源，我们提出了一个洛伦兹协变，真正的制定中，第二类约束永远不会出现。我们使用一个规范场y，而不是时空的叶理，它被解释为一个观察者场，将SO（3，1）对称性破缺为一个子群SO（3）_y。这种对称性破缺所起的作用类似于麦克道尔-曼苏尔引力，后者是以嘉当几何为基础的，这将我们引向一幅引力的图景，即“嘉当几何动力学”。“我们研究了洛伦兹规范变换和观测者场的变换，以表明SO（3，1）到SO（3）的明显破缺与洛伦兹协方差不冲突。
英文摘要：
In Ashtekar's Hamiltonian formulation of general relativity, and in loop quantum gravity, Lorentz covariance is a subtle issue that has been strongly debated. Maintaining manifest Lorentz covariance seems to require introducing either complex-valued fields, presenting a significant obstacle to quantization, or additional (usually second class) constraints whose solution renders the resulting phase space variables harder to interpret in a spacetime picture. After reviewing the sources of difficulty, we present a Lorentz covariant, real formulation in which second class constraints never arise. Rather than a foliation of spacetime, we use a gauge field y, interpreted as a field of observers, to break the SO(3,1) symmetry down to a subgroup SO(3)_y. This symmetry breaking plays a role analogous to that in MacDowell-Mansouri gravity, which is based on Cartan geometry, leading us to a picture of gravity as 'Cartan geometrodynamics.' We study both Lorentz gauge transformations and transformations of the observer field to show that the apparent breaking of SO(3,1) to SO(3) is not in conflict with Lorentz covariance.
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