Wheeler-DeWitt Equation and the Applicability of Crypto-Hermitian Interaction Representation in Quantum Cosmology

Abstract

In the broader methodical framework of the quantization of gravity, the crypto-Hermitian (or non-Hermitian) version of Dirac's interaction picture is considered. The formalism is briefly outlined and shown to be well suited for an innovative treatment of certain cosmological models. In particular, it is demonstrated that the Wheeler-DeWitt equation could be a promising candidate for the description of the evolution of the quantized Universe near its initial Big Bang singularity.