478 research outputs found
Higher-Order Differential Operators on a Lie Group and Quantization
This talk is devoted mainly to the concept of higher-order polarization on a
group, which is introduced in the framework of a Group Approach to
Quantization, as a powerful tool to guarantee the irreducibility of
quantizations and/or representations of Lie groups in those anomalous cases
where the Kostant-Kirilov co-adjoint method or the Borel-Weyl-Bott
representation algorithm do not succeed.Comment: 9 pages, latex, no figures, uses IJMPB.sty (included). New version
partially rewritten (title changed!), presented to the II Int. Workshop on
Class. and Quant. Integrable Systems, Dubna (Rusia) 1996, and published in
Int. J. Mod. Phys.
Alternative Hamiltonian Desciptions and Statistical Mechanics
We argue here that, as it happens in Classical and Quantum Mechanics, where
it has been proven that alternative Hamiltonian descriptions can be compatible
with a given set of equations of motion, the same holds true in the realm of
Statistical Mechanics, i.e. that alternative Hamiltonian descriptions do lead
to the same thermodynamical description of any physical system.Comment: 11 page
Tomography on f-oscillators
Symplectic tomographies of classical and quantum states are shortly reviewed.
The concept of nonlinear f-oscillators and their properties are recalled. The
tomographic probability representations of oscillator coherent states and the
problem of entanglement are then discussed. The entanglement of even and odd
f-coherent states is evaluated by the linear entropy
Completely integrable systems: a generalization
We present a slight generalization of the notion of completely integrable
systems to get them being integrable by quadratures. We use this generalization
to integrate dynamical systems on double Lie groups.Comment: Latex, 15 page
Remarks on the star product of functions on finite and compact groups
Using the formalism of quantizers and dequantizers, we show that the
characters of irreducible unitary representations of finite and compact groups
provide kernels for star products of complex-valued functions of the group
elements. Examples of permutation groups of two and three elements, as well as
the SU(2) group, are considered. The k-deformed star products of functions on
finite and compact groups are presented. The explicit form of the quantizers
and dequantizers, and the duality symmetry of the considered star products are
discussed.Comment: 17 pages, minor changes with respect to the published version of the
pape
Tomographic map within the framework of star-product quantization
Tomograms introduced for the description of quantum states in terms of
probability distributions are shown to be related to a standard star-product
quantization with appropriate kernels. Examples of symplectic tomograms and
spin tomograms are presented.Comment: LATEX plus sprocl.sty, to appear in the Proceedings of the conference
``Quantum Theory and Symmetries'' (Krakow, July 2001), World Scietifi
Superintegrability in the Manev Problem and its Real Form Dynamics
We report here the existence of Ermanno-Bernoulli type invariants for the
Manev model dynamics which may be viewed upon as remnants of Laplace-Runge-Lenz
vector whose conservation is characteristic of the Kepler model. If the orbits
are bounded these invariants exist only when a certain rationality condition is
met and thus we have superintegrability only on a subset of initial values. We
analyze real form dynamics of the Manev model and derive that it is always
superintegrable. We also discuss the symmetry algebras of the Manev model and
its real Hamiltonian form.Comment: 12 pages, LaTeX, In: Prof. G. Manev's Legacy in Contemporary
Astronomy, Theoretical and Gravitational Physics, V. Gerdjikov, M. Tsvetkov
(Eds), Heron Press, Sofia 2005, pp. 155-16
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