—The paper is devoted to some of the difficulties which the Wheeler-DeWitt quantum geometrodynamics encountered, in particular, a strong mathematical proof that this theory is gauge-invariant, the definition of the wave function of the Universe through a path integral and the illegality of asymptotic boundary conditions in quantum gravity, the derivation of the Wheeler-DeWitt equation from the path integral and the equivalence of the Dirac quantization scheme with other approaches, the problem of definition of physical states in quantum gravity, possible realizations of the Everett concept of “relative states.” These problems are rarely discussed in the literature. They are related to the guiding idea that quantum theory of gravity must be gauge-invariant. It will lead to the question if it is possible to achieve this goal in a mathematically consistent way.

中文翻译：

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宇宙的波动函数，路径积分和量规不变性

-本文专门研究了惠勒-德威特量子地球动力学所遇到的一些困难，特别是有力的数学证据证明了该理论是尺度不变的，通过路径积分定义了宇宙的波函数，并且发现了违法性量子引力中的渐近边界条件，Wheeler-DeWitt方程从路径积分推导，Dirac量化方案与其他方法的等价性，量子引力中的物理状态定义问题，Everett概念的可能实现“相对状态”。这些问题很少在文献中讨论。它们与指导思想有关，即引力量子理论必须是尺度不变的。