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

**Miloslav Znojil 1,2**


**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.

**Keywords:** quantum gravity and the problem of the Big Bang; hidden Hermitian formulations of quantum mechanics; stationary Wheeler–DeWitt system; physical Hilbert space metric; non-stationary Wheeler–DeWitt system
