Simple Approach to Quantization of the Gravitational Field - Strumia, Alberto (New Trends in Physical Science Research Vol. 6, 2022)
Due to the non-linearity of the Einstein equations, we provide a simple way to approach the difficult problem of quantization of the gravitational field in four dimensions space-time. When the cosmological constant is not null, the problem may be solved. Quantization will be performed on the Hamiltonian of the cosmological part, so providing quantization also of the opposite Riemannian part. When the cosmological contribution is treated as the energy-momentum of vacuum, and the metric tensor is represented on the tetrad of its eigenvectors, the corresponding energy-momentum and, as a result, the Hamiltonian, can be easily quantized using a correspondence rule in which the eigenvectors are replaced by creation and annihilation operators for the gravitational field. As a result, the geometric Einstein tensor is quantized, which has the same sign as the vacuum energy-momentum (plus the potentially known matter one). We look at physical examples offered by Schwarzschild-DeSitter, Robertson-Walker-DeSitter, and Kerr-DeSitter solutions.