Wheeler-DeWitt equation and the applicability of crypto-Hermitian interaction representation in quantum cosmology

Abstract

Recently, Wang with Stankiewicz (Phys. Lett. B 800 (2020) 135106) opposed the widespread belief that due to quantization, the Big Bang singularity {\em must} necessarily get smeared and replaced by a non-singular "Big Bounce" process. Their claim is supported in a methodically independent manner in which just a highly schematic model (viz., the discrete and drastically simplified Wheeler-DeWitt equation) is considered. Our comparatively elementary argumentation is constructive, based on the assumption that the evolution of the Universe can fully consistently be described using an innovative, hiddenly Hermitian version of quantum theory formulated in a properly upgraded Dirac's interaction picture.

33 pp., 3 pictures

References in corpus (15)

• Making Sense of Non-Hermitian Hamiltonians
• Quantum Nature of the Big Bang: Improved dynamics
• A Short Review of Loop Quantum Gravity
• Time-dependent version of cryptohermitian quantum theory
• Three-Hilbert-Space Formulation of Quantum Mechanics
• Quantum nature of cosmological bounces
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
• Adiabatic time-dependent metrics in PT-symmetric quantum theories
• Non-Hermitian Heisenberg representation
• Matrix Hamiltonians with an algebraic guarantee of unbroken PT-symmetry
• Quantization of time and the big bang via scale-invariant loop gravity
• Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians

Cited by in corpus (10)

• Hybrid form of quantum theory with non-Hermitian Hamiltonians
• Systematics of quasi-Hermitian representations of non-Hermitian quantum models
• Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions
• Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation
• Non-Hermitian-Hamiltonian-induced unitarity and optional physical inner products in Hilbert space
• Interference of non-Hermiticity with Hermiticity at exceptional points
• Three alternative model-building strategies using quasi-Hermitian time-dependent observables
• Comment on 'The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'
• Quantum Quintom Cosmology