deformation of Calogero-Sutherland model via dimensional reduction
arXiv:2111.12080
Abstract
We perform the dynamical change of coordinates to derive a generalization of the trace relation and apply it to the non-linear Schrödinger model. After that, we work out the dimensional reduction of the bilinear operator and obtain the new -like deformation of the quantum mechanics of free non-relativistic fermions and interacting Calogero-Sutherland particles. The deformation modifies the spectrum of the Hamiltonian but does not alter its eigenfunctions. The deformed classical Lagrangian is also obtained. Finally, we study a particular deformation of the two-dimensional Yang-Mills theory that maps the gauge theory onto a system of -perturbed fermions.
10 pages, 1 figure; v4