Quantum $SU(2,2)$-Harmonic Oscillator

Abstract

The $SU(2,2)$-harmonic oscillator on the phase space $\mathcal{A}(2,2)=SU(2,2)/S(U(2)\times U(2))$ is quantized using the coherent states. The quantum Hamiltonian is the Toeplitz operator corresponding to the square of the distance with respect to the $SU(2,2)$-invariant Kähler metric on the phase space. Its spectrum, depending on the choice of representation of $SU(2,2)$, is computed.

10 pages, LaTex file

References in corpus (1)

• Quantum $SU(2,2)$-Harmonic Oscillator

Cited by in corpus (2)

• Quantum $SU(2,2)$-Harmonic Oscillator
• Approach of the Generating Functions to the Coherent States for Some Quantum Solvable Models