Conformal bridge between asymptotic freedom and confinement

• URL: http://arxiv.org/abs/1912.11752v3
• Date: Sat, 30 May 2020 06:29:33 GMT
• Title: Conformal bridge between asymptotic freedom and confinement
• Authors: Luis Inzunza, Mikhail S. Plyushchay, Andreas Wipf
• Abstract summary: We construct a nonunitary transformation that relates a given "asymptotically free" conformal quantum mechanical system $H_f$ with its confined, harmonically trapped version $H_c$. We investigate the one- and two-dimensional examples that reveal, in particular, a curious relation between the two-dimensional free particle and the Landau problem.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct a nonunitary transformation that relates a given "asymptotically free" conformal quantum mechanical system $H_f$ with its confined, harmonically trapped version $H_c$. In our construction, Jordan states corresponding to the zero eigenvalue of $H_f$, as well as its eigenstates and Gaussian packets are mapped into the eigenstates, coherent states and squeezed states of $H_c$, respectively. The transformation is an automorphism of the conformal $\mathfrak{sl}(2,{\mathbb R})$ algebra of the nature of the fourth-order root of the identity transformation, to which a complex canonical transformation corresponds on the classical level being the fourth-order root of the spatial reflection. We investigate the one- and two-dimensional examples that reveal, in particular, a curious relation between the two-dimensional free particle and the Landau problem.

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