SU(2) Action-Angle Variables
Demosthenes Ellinas
TL;DR
This paper explores the formulation of operator angle-action variables within the SU(2) algebra, revealing their eigenstates, coherent states, and a novel non-commutative Hopf algebra, with connections to the harmonic oscillator via group contraction.
Contribution
It introduces a new framework for angle-action variables in SU(2), including their algebraic structure and relation to harmonic oscillators.
Findings
Eigenstates and coherent states of SU(2) angle-action variables are characterized.
A new non-commutative Hopf algebra arising from quantum addition is identified.
Group contraction links SU(2) variables to harmonic oscillator models.
Abstract
Operator angle-action variables are studied in the frame of the SU(2) algebra, and their eigenstates and coherent states are discussed. The quantum mechanical addition of action-angle variables is shown to lead to a novel non commutative Hopf algebra. The group contraction is used to make the connection with the harmonic oscillator.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Algebraic structures and combinatorial models · Advanced Topics in Algebra