Conformal bridge between asymptotic freedom and confinement

Luis Inzunza, Mikhail S. Plyushchay, Andreas Wipf
2020 Physical Review D  
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 slð2; RÞ algebra of the nature of the
more » ... -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.
doi:10.1103/physrevd.101.105019 fatcat:a7uk5dubujal5o6qk3vqtzhc4e