190 research outputs found
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
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
On particle dynamics in AdS_{N+1} space-time
We summarize part of a systematic study of particle dynamics on
space-time based on Hamiltonian methods. New explicit UIR's of SO(2,N), defined
on certain spaces of holomorphic functions, are constructed. The connection to
some field theoretic results, including the construction of propagators, is
discussed.Comment: 8 pages, to appear in the proceedings of the 37th Int. Symp.
Ahrenshoop on the Theory of Elementary Particles, Aug. 23-27, 2004,
Berlin-Schm\"ockwit
Constrained Quantization on Symplectic Manifolds and Quantum Distribution Functions
A quantization scheme based on the extension of phase space with application
of constrained quantization technic is considered. The obtained method is
similar to the geometric quantization. For constrained systems the problem of
scalar product on the reduced Hilbert space is investigated and possible
solution of this problem is done. Generalization of the Gupta-Bleuler like
conditions is done by the minimization of quadratic fluctuations of quantum
constraints. The scheme for the construction of generalized coherent states is
considered and relation with Berezin quantization is found. The quantum
distribution functions are introduced and their physical interpretation is
discussed.Comment: 42 page
Correlation Functions and Vertex Operators of Liouville Theory
We calculate correlation functions for vertex operators with negative integer
exponentials of a periodic Liouville field, and derive the general case by
continuing them as distributions. The path-integral based conjectures of Dorn
and Otto prove to be conditionally valid only. We formulate integral
representations for the generic vertex operators and indicate structures which
are related to the Liouville S-matrix.Comment: 9 pages, LaTe
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
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
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