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

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

1999-12-02

arxiv.org/abs/gr-qc/9912006v1

Phys.Lett. B476 (2000) 134-140

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, LaTeX2e, no figures

Scientific paper

10.1016/S0370-2693(00)00116-7

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 $L^2(S^{N-1})$.

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