论文标题
在没有度量的情况下搜索重力
Searching for Gravity Without a Metric
论文作者
论文摘要
最近，它已经明确显示了具有全局$ gl（d，\ mathbb {r}）$坐标（仿射）不变性的理论如何自发地分解为Lorentz子组的戈德石领域，足以创建一个指标和协证的导数arxiv：1105.5888。这种理论将构成一个有效的重力理论。然而，到目前为止，尚未发现任何明确的理论表现出这种对称性破坏模式，这主要是由于很难写下$ gl（d，\ mathbb {r}）$不变动作在没有度量的情况下。在本文中，我们明确地构建了采用该组的无限尺寸旋转表示的狄拉克动作的仿射概括。这意味着它是由无限数量的旋转洛伦兹多重组构建的。我们介绍了一个系统的过程，用于获取$ gl（d，\ mathbb {r}）$不变交互项以获取相当一般的交互模型。这样的模型具有订单运算符，其期望值可以打破对称对称性的仿射对称性。我们讨论了发生这种对称性破坏的可能相互作用和机制，这将提供对时空的洛伦兹（Lorentzian）特征的动态解释。
Recently it has been explicitly shown how a theory with global $GL(d,\mathbb{R})$ coordinate (affine) invariance which is spontaneously broken down to its Lorentz subgroup will have as its Goldstone fields enough degrees of freedom to create a metric and a covariant derivative arXiv:1105.5848. Such a theory would constitute an effective theory of gravity. So far however, no explicit theory has been found which exhibits this symmetry breaking pattern, mainly due to the difficulty of even writing down a $GL(d,\mathbb{R})$ invariant actions in the absence of a metric. In this paper we explicitly construct an affine generalization of the Dirac action employing infinite dimensional spinorial representations of the group. This implies that it is built from an infinite number of spinor Lorentz multiplets. We introduce a systematic procedure for obtaining $GL(d,\mathbb{R})$ invariant interaction terms to obtain quite general interacting models. Such models have order operators whose expectation value can break affine symmetry to Poincaré symmetry. We discuss possible interactions and mechanisms for this symmetry breaking to occur, which would provide a dynamical explanation of the Lorentzian signature of spacetime.
