Abstract

Covariant perturbation theory allows one to calculate the nonlocal kernel of the evolution equation on a spin Riemannian manifold. The proposed axiomatic definition of effective action introduces a universal scale parameter with the dimension of the square of the distance into the dimensionless mathematical theory. It is shown that this purely geometric result has the physical meaning of the action of field theory, including gravity. The two lowest tensor orders of this covariant functional are independent of the type of the spin group and are local; they reproduce the action of general relativity with a cosmological constant. The modern value of the universal distance scale can be determined by the measured Hubble constant. This scale parameter, considered a physical variable, makes it possible to construct the cosmological theory axiomatically.

中文翻译：

---

重力理论中演化方程的内核方法

摘要

协变摄动理论允许人们在自旋黎曼流形上计算演化方程的非局部核。所提出的有效行动的公理式定义将无距离数学理论中具有距离平方的维数的通用比例参数引入。结果表明，这种纯粹的几何结果具有包括重力在内的场论作用的物理意义。此协变函数的两个最低张量阶数与自旋基团的类型无关，并且是局部的。它们以宇宙学常数再现广义相对论的作用。通用距离标尺的现代值可以通过测得的哈勃常数来确定。这个标度参数，被认为是一个物理变量，使得有可能公理地构建宇宙学理论。