A non-perturbative and background-independent quantum formulation of quadratic gravity is provided. A canonical quantization procedure introduced in previous works, named after Dirac and Pauli, is here applied to quadratic gravity to obtain, as required by consistency, a well-defined Euclidean path integral. The theory is unitary: all probabilities are non negative and they sum up to one. We obtain path-integral expressions for the transition amplitudes, Green's functions and generic matrix elements of time-ordered products of the metric. As a byproduct, similar results are also obtained for a scalar-field four-derivative interacting model. In this way, among other things, previous perturbative and background-dependent calculations are justified. The (quantum) quadratic gravity effective action, whose field equations determine the vacuum expectation value of the metric in the presence of a generic energy-momentum tensor, is constructed. The classical limit of the effective action turns out to be equivalent to the starting classical action of quadratic gravity, whose runaway rates were previously shown to be slow enough to be compatible with observations. Finally, the constructed non-perturbative and background-independent quantum quadratic gravity is applied to quantum cosmology to obtain a path-integral expression for the wave function of the universe, which satisfies a sort of Wheeler-DeWitt equation. This application allows us to understand at the quantum level why our universe is nearly homogeneous and isotropic.

中文翻译：

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二次引力的非微扰且与背景无关的公式


提供了二次引力的非微扰且与背景无关的量子公式。以前的作品中引入的规范量化过程（以狄拉克和泡利的名字命名）在这里应用于二次引力，以获得一致性要求的明确定义的欧几里得路径积分。该理论是统一的：所有概率都是非负的，并且它们的总和为一。我们获得了过渡幅度的路径积分表达式、格林函数和度量的时间排序乘积的通用矩阵元素。作为副产品，标量场四导数相互作用模型也获得了类似的结果。通过这种方式，除其他外，先前的扰动和背景相关的计算是合理的。构造了（量子）二次重力有效作用，其场方程确定了在存在通用能量动量张量的情况下度量的真空期望值。有效作用的经典极限相当于二次引力的起始经典作用，其失控率先前已被证明足够慢，足以与观测结果兼容。最后，将构造的非微扰且背景无关的量子二次引力应用于量子宇宙学，得到满足某种Wheeler-DeWitt方程的宇宙波函数的路径积分表达式。这个应用程序使我们能够在量子水平上理解为什么我们的宇宙几乎是均匀且各向同性的。