Geometry of 2d spacetime and quantization of particle dynamics

Abstract

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 $S{O}_{\uparrow }(2.1)$ group.

12 pages, LaTeX2e, submitted for publication

References in corpus (2)

• Massless particle in 2d spacetime with constant curvature
• Dynamical Ambiguities in Singular Gravitational Field

Cited by in corpus (7)

• Quantization and spacetime topology
• Oscillator quantization of the massive scalar particle dynamics on AdS spacetime
• Quantum particle on hyperboloid
• Pseudospherical functions on a hyperboloid of one sheet
• On particle dynamics in AdS_{N+1} space-time
• Families of exact solutions of a 2D gravity model minimally coupled to electrodynamics
• Particle dynamics on hyperboloid and unitary representation of SO(1,N) group