Representation theory of $\mathfrak{sl}(2,\mathbb{R})\simeq \mathfrak{su}(1,1)$ and a generalization of non-commutative harmonic oscillators

Ryosuke Nakahama

The non-commutative harmonic oscillator (NCHO) was introduced as a specific Hamiltonian operator on $L^2(\mathbb{R})\otimes {\mathbb{C}}^2$ by Parmeggiani and Wakayama. Then it was pr…