Multi Parametric Deformed Heisenberg Algebras: A Route to Complexity

Simple item page
dc.creatorCurado, E. M. F.
dc.creatorRego-Monteiro, M. A.
dc.date2000-11-14
dc.date2001-03-05
dc.date.accessioned2026-07-07T10:53:28Z
dc.date.available2026-07-07T10:53:28Z
dc.descriptionWe introduce a generalization of the Heisenberg algebra which is written in terms of a functional of one generator of the algebra, $f(J_0)$, that can be any analytical function. When $f$ is linear with slope $θ$, we show that the algebra in this case corresponds to $q$-oscillators for $q^2 = \tan θ$. The case where $f$ is a polynomial of order $n$ in $J_0$ corresponds to a $n$-parameter deformed Heisenberg algebra. The representations of the algebra, when $f$ is any analytical function, are shown to be obtained through the study of the stability of the fixed points of $f$ and their composed functions. The case when $f$ is a quadratic polynomial in $J_0$, the simplest non-linear scheme which is able to create chaotic behavior, is analyzed in detail and special regions in the parameter space give representations that cannot be continuously deformed to representations of Heisenberg algebra.
dc.descriptionlatex, 17 pages, 5 PS figures; to be published in J. Phys. A: Math and Gen (2001); a few sentences were added in order to clarify some points
dc.identifierhttps://arxiv.org/abs/hep-th/0011126
dc.identifierhttp://arxiv.org/abs/hep-th/0011126
dc.identifierJ.Phys.A34:3253-3264,2001
dc.identifierdoi:10.1088/0305-4470/34/15/304
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185495
dc.subjectHigh Energy Physics - Theory
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.subjectQuantum Physics
dc.titleMulti Parametric Deformed Heisenberg Algebras: A Route to Complexity
dc.typetext

Files

Collections

arXiv