819 research outputs found
Symmetry Duality: Exploring Exotic Oscillators And Dissipative Dynamics Through The Glass Of Newton-Hooke
Motivated by the symmetry in the non-relativistic limit of anti-de Sitter
geometry, we employ planar dynamical models featuring exotic (deformed)
harmonic oscillators, presented through direct and indirect Lagrangian
representations. The latter introduces Bateman dissipative oscillator system.
Analyzing these dynamic systems with a first-order Lagrangian scheme, our
phase-space-based approach utilizes the moment map components to reveal the
underlying symmetry algebra. This obtained algebra, interpreted as an extended
version of Newton-Hooke (NH) cosmological symmetry algebras, has the potential
to cast an augmented non-relativistic shadow over the expanding universe,
offering an insightful perspective on extended NH spacetime in 2+1 dimensions
through our dynamical realizations
Particle Dynamics and Lie-algebraic type of Non-commutativity of space-time
In this paper, we present the results of our investigation relating particle
dynamics and non-commutativity of space-time by using Dirac's constraint
analysis. In this study, we re-parameterise the time along with
and treat both as configuration space variables. Here, is a
monotonic increasing parameter and the system evolves with this parameter.
After constraint analysis, we find the deformed Dirac brackets similar to the
-deformed space-time and also, get the deformed Hamilton's equations of
motion. Moreover, we study the effect of non-commutativity on the generators of
Galilean group and Poincare group and find undeformed form of the algebra.
Also, we work on the extended space analysis in the Lagrangian formalism. We
find the primary as well as the secondary constraints. Strikingly on
calculating the Dirac brackets among the phase space variables, we obtain the
classical version of -Minkowski algebra.Comment: 15 page
- …