arXiv subjects

Włodzimierz Piechocki

Publications and source records attributed to Włodzimierz Piechocki.

21 records · Page 2Linked to original sources

arXiv2014

Quantum theory of the Bianchi II model

We describe the quantum evolution of the vacuum Bianchi II universe in terms of the transition amplitude between two asymptotic quantum Kasner-like states. For large values of the momentum variable the classical and quantum calculations give similar results. The difference occurs for small values of this variable due to the Heisenberg uncertainty principle. Our results can be used, to some extent, as a building block of the quantum evolution of the vacuum Bianchi IX universe.

gr-qc↗

arXiv1999

Massless particle in 2d spacetime with constant curvature

We consider dynamics of massless particle in 2d spacetimes with constant curvature. We analyze different examples of spacetime. Dynamical integrals are constructed from spacetime symmetry related to $sl(2.{\bf R})$ algebra. Mass-shell condition restricts dynamical integrals to a cone (without vertex) which defines physical-phase space. We parametrize the cone by canonical coordinates. Canonical quantization with definite choice of operator ordering leads to unitary irreducible representations of $SO_\uparrow (2.1)$ group.

hep-th↗

arXiv1998

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.

gr-qc↗