43 research outputs found
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 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 dimensional one-sheet hyperboloid
embedded in dimensional Minkowski space. The dynamical integrals
constructed by 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 group on Hilbert space
.Comment: 12 pages, LaTeX2e, no figure
Quantization of the Superparticle on
We analyze superparticle dynamics on the coset . The system is quantized in
canonical coordinates obtained by gauge invariant Hamiltonian reduction. The
left and right Noether charges of a massive particle are parametrized by
coadjoint orbits of a timelike element of . Each chiral sector
is described by two bosonic and two fermionic canonical coordinates
corresponding to a superparticle with superpotential , where is
the particle mass. Canonical quantization then provides a quantum realization
of . For the massless particle the chiral
charges lie on the coadjoint orbit of a nilpotent element of
and each of them depends only on one real fermion, which demonstrates the
underlying -symmetry. These remaining left and right fermionic
variables form a canonical pair and the system is described by four bosonic and
two fermionic canonical coordinates. Due to conformal invariance of the
massless particle, the extends to the
corresponding superconformal algebra . Its 19 charges are
given by all real quadratic combinations of the canonical coordinates, which
trivializes their quantization.Comment: 25+1 pages; v2: minor changes, references added and updated; v3:
minor changes, one reference added, matches published versio
Oscillator quantization of the massive scalar particle dynamics on AdS spacetime
The set of trajectories for massive spinless particles on
spacetime is described by the dynamical integrals related to the isometry group
SO(2,N). The space of dynamical integrals is mapped one to one to the phase
space of the -dimensional oscillator. Quantizing the system canonically, the
classical expressions for the symmetry generators are deformed in a consistent
way to preserve the commutation relations. This quantization thus
yields new explicit realizations of the spin zero positive energy UIR's of
SO(2,N) for generic . The representations as usual can be characterized by
their minimal energy and are valid in the whole range of
allowed by unitarity.Comment: Latex, 14 pages, version to appear in PL