On the dynamics of the general Bianchi IX spacetime near the singularity

We show that the complex dynamics of the general Bianchi IX universe in the vicinity of the spacelike singularity can be approximated by a simplified system of equations. Our analysis is mainly based on numerical simulations. The properties of the solution space can be studied by using this simplified dynamics. Our results will be useful for the quantization of the general Bianchi IX model.Comment: 20 pages, 5 figures, minor change

Geometry of 2d spacetime and quantization of particle dynamics

We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space and the corresponding quantum theory. To quantize the systems we parametrize the physical phase-space by canonical coordinates. Canonical quantization leads to unitary irreducible representations of $SO_\uparrow (2.1)$ group.Comment: 12 pages, LaTeX2e, submitted for publicatio

Particle dynamics on hyperboloid and unitary representation of SO(1,N) group

We analyze particle dynamics on $N$ dimensional one-sheet hyperboloid embedded in $N+1$ dimensional Minkowski space. The dynamical integrals constructed by $SO_\uparrow (1,N)$ symmetry of spacetime are used for the gauge-invariant Hamiltonian reduction. The physical phase-space parametrizes the set of all classical trajectories on the hyperboloid. In quantum case the operator ordering problem for the symmetry generators is solved by transformation to asymptotic variables. Canonical quantization leads to unitary irreducible representation of $SO_\uparrow (1,N)$ group on Hilbert space $L^2(S^{N-1})$.Comment: 12 pages, LaTeX2e, no figure

Quantum Belinski-Khalatnikov-Lifshitz scenario

We present the quantum model of the asymptotic dynamics underlying the Belinski-Khalatnikov-Lifshitz (BKL) scenario. The symmetry of the physical phase space enables making use of the affine coherent states quantization. Our results show that quantum dynamics is regular in the sense that during quantum evolution the expectation values of all considered observables are finite. The classical singularity of the BKL scenario is replaced by the quantum bounce that presents a unitary evolution of considered gravitational system. Our results suggest that quantum general relativity is free from singularities.Comment: 33 pages, 4 figures, version accepted for publication in European Physical Journal C. arXiv admin note: substantial text overlap with arXiv:1705.0402

Singular spacetime and quantum probe

We examine the dependence of quantization on global properties of a classical system. Quantization based on local properties may lead to ambiguities and inconsistency between local and global symmetries of a quantum system. Our quantization method based on global characteristics has sound foundation. Presented results give insight into the nature of removable type singularity of spacetime at the quantum level.Comment: 9 pages, latex2e, no figures; to appear in Phys.Lett.