Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-09-16
Int.J.Theor.Phys.50:955-962,2011
Physics
High Energy Physics
High Energy Physics - Theory
8 pages, 7 figures
Scientific paper
10.1007/s10773-010-0511-2
The E2 algebra has three elements, J, u, and v, which satisfy the commutation relations [u,J]=iv, [v,J]=-iu, [u,v]=0. We can construct the Hamiltonian H=J^2+gu, where g is a real parameter, from these elements. This Hamiltonian is Hermitian and consequently it has real eigenvalues. However, we can also construct the PT-symmetric and non-Hermitian Hamiltonian H=J^2+igu, where again g is real. As in the case of PT-symmetric Hamiltonians constructed from the elements x and p of the Heisenberg algebra, there are two regions in parameter space for this PT-symmetric Hamiltonian, a region of unbroken PT symmetry in which all the eigenvalues are real and a region of broken PT symmetry in which some of the eigenvalues are complex. The two regions are separated by a critical value of g.
Bender Carl M.
Kalveks R. J.
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