Wave function of the Universe, path integrals and gauge invariance
arXiv:1912.09182 · doi:10.1134/S0202289319040121
Abstract
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". The problems are rarely discussed in the literature. They are related with the guiding idea that quantum theory of gravity must gauge invariant. It will lead to the question if it is possible to achieve this goal in a mathematically consistent way.
12 pages, the paper was written for the hundredth issue of the journal "Gravitation & Cosmology"
References in corpus (4)
- The strange equation of quantum gravity
- Is the Wheeler -- DeWitt equation more fundamental than the Schrödinger equation?
- The problem of time and gauge invariance in the quantization of cosmological models. II. Recent developments in the path integral approach
- The problem of time and gauge invariance in the quantization of cosmological models. I. Canonical quantization methods