Algebraic analysis of the two-dimensional Higgs oscillator and nonlinear coherent states

Abstract The two-dimensional Higgs oscillator, defined on the surface of a sphere <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">S</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> , can be mapped via a stereographic projection to a conformally transformed harmonic oscillator on the complex plane. Its quantum mechanical exact solvability provides the foundation for subsequent analyses, including the study of dual SUSY partners and the construction of continuous-variable quantum states. Due to the non-standard form of its Hamiltonian, factorization is complex, and the corresponding ladder operators are deformed. Furthermore, algebraic analysis reveals that the system satisfies the su (1, 1) algebra, which allows for the construction of Perelomov and Barut-Girardello nonlinear coherent states.