Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-11-14
J.Phys.A34:3253-3264,2001
Physics
High Energy Physics
High Energy Physics - Theory
latex, 17 pages, 5 PS figures; to be published in J. Phys. A: Math and Gen (2001); a few sentences were added in order to clar
Scientific paper
10.1088/0305-4470/34/15/304
We 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 $\theta$, we show that the algebra in this case corresponds to $q$-oscillators for $q^2 = \tan \theta$. 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.
Curado Evaldo M. F.
Rego-Monteiro Marco Aurelio
No associations
LandOfFree
Multi Parametric Deformed Heisenberg Algebras: A Route to Complexity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multi Parametric Deformed Heisenberg Algebras: A Route to Complexity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multi Parametric Deformed Heisenberg Algebras: A Route to Complexity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-251129