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${\cal PT}$ deformation of angular Calogero models. (arXiv:1705.05425v1 [hep-th])
来源于:arXiv
The rational Calogero model based on an arbitrary rank-$n$ Coxeter root
system is spherically reduced to a superintegrable angular model of a particle
moving on $S^{n-1}$ subject to a very particular potential singular at the
reflection hyperplanes. It is outlined how to find conserved charges and to
construct intertwining operators. We deform these models in a ${\cal
PT}$-symmetric manner by judicious complex coordinate transformations, which
render the potential less singular. The ${\cal PT}$ deformation does not change
the energy eigenvalues but in some cases adds a previously unphysical tower of
states. For integral couplings the new and old energy levels coincide, which
roughly doubles the previous degeneracy and allows for a conserved nonlinear
supersymmetry charge. We present the details for the generic rank-two ($A_2$,
$G_2$) and all rank-three Coxeter systems ($AD_3$, $BC_3$ and $H_3$), including
a reducible case ($A_1^{\otimes 3}$). 查看全文>>