sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues

Details sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues

2000-08-10

arxiv.org/abs/math-ph/0008020v1

Phys.Lett. A273 (2000) 285-292

Physics

Mathematical Physics

LaTeX, amssym,14 pages, no figures, to be published in Phys. Lett. A

Scientific paper

10.1016/S0375-9601(00)00512-0

The powerful group theoretical formalism of potential algebras is extended to
non-Hermitian Hamiltonians with real eigenvalues by complexifying so(2,1),
thereby getting the complex algebra sl(2,\C) or $A_1$. This leads to new types
of both PT-symmetric and non-PT-symmetric Hamiltonians.

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