https://doi.org/10.1140/epjc/s10052-024-12662-4
Regular Article - Theoretical Physics
Symmetry harmonization: exploring deformed oscillators and dissipative dynamics through the glass of Newton–Hooke algebra
1
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, 700108, Kolkata, West Bengal, India
2
Department of Physics, University of Stellenbosch, 7600, Stellenbosch, South Africa
Received:
23
January
2024
Accepted:
11
March
2024
Published online:
24
March
2024
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.
© The Author(s) 2024
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