650 research outputs found
Quantization with Action-Angle Coherent States
For a single degree of freedom confined mechanical system with given energy,
we know that the motion is always periodic and action-angle variables are
convenient choice as conjugate phase-space variables. We construct action-angle
coherent states in view to provide a quantization scheme that yields precisely
a given observed energy spectrum for such a system. This construction
is based on a Bayesian approach: each family corresponds to a choice of
probability distributions such that the classical energy averaged with respect
to this probability distribution is precisely up to a constant shift. The
formalism is viewed as a natural extension of the Bohr-Sommerfeld rule and an
alternative to the canonical quantization. In particular, it also yields a
satisfactory angle operator as a bounded self-adjoint operator
A natural fuzzyness of de Sitter space-time
A non-commutative structure for de Sitter spacetime is naturally introduced
by replacing ("fuzzyfication") the classical variables of the bulk in terms of
the dS analogs of the Pauli-Lubanski operators. The dimensionality of the fuzzy
variables is determined by a Compton length and the commutative limit is
recovered for distances much larger than the Compton distance. The choice of
the Compton length determines different scenarios. In scenario I the Compton
length is determined by the limiting Minkowski spacetime. A fuzzy dS in
scenario I implies a lower bound (of the order of the Hubble mass) for the
observed masses of all massive particles (including massive neutrinos) of spin
s>0. In scenario II the Compton length is fixed in the de Sitter spacetime
itself and grossly determines the number of finite elements ("pixels" or
"granularity") of a de Sitter spacetime of a given curvature.Comment: 16 page
A discrete nonetheless remarkable brick in de Sitter: the "massless minimally coupled field"
Over the last ten years interest in the physics of de Sitter spacetime has
been growing very fast. Besides the supposed existence of a "de sitterian
period" in inflation theories, the observational evidence of an acceleration of
the universe expansion (interpreted as a positive cosmological constant or a
"dark energy" or some form of "quintessence") has triggered a lot of attention
in the physics community. A specific de sitterian field called "massless
minimally coupled field" (mmc) plays a fundamental role in inflation models and
in the construction of the de sitterian gravitational field. A covariant
quantization of the mmc field, `a la Krein-Gupta-Bleuler was proposed in [1].
In this talk, we will review this construction and explain the relevance of
such a field in the construction of a massless spin 2 field in de Sitter
space-time.Comment: Proceedings of the XXVII Colloquium on Group Theoretical Methods in
Physics, Yerevan, August 200
Coherent state quantization of paragrassmann algebras
By using a coherent state quantization of paragrassmann variables, operators
are constructed in finite Hilbert spaces. We thus obtain in a straightforward
way a matrix representation of the paragrassmann algebra. This algebra of
finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean
values in coherent states of some of these operators lead to interesting
conclusions.Comment: We provide an erratum where we improve upon our previous definition
of odd paragrassmann algebra
Examples of Berezin-Toeplitz Quantization: Finite sets and Unit Interval
We present a quantization scheme of an arbitrary measure space based on
overcomplete families of states and generalizing the Klauder and the
Berezin-Toeplitz approaches. This scheme could reveal itself as an efficient
tool for quantizing physical systems for which more traditional methods like
geometric quantization are uneasy to implement. The procedure is illustrated by
(mostly two-dimensional) elementary examples in which the measure space is a
-element set and the unit interval. Spaces of states for the -element set
and the unit interval are the 2-dimensional euclidean and hermitian
\C^2 planes
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