sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
classification
🧮 math-ph
math.MPquant-ph
keywords
hamiltoniansalgebracomplexeigenvaluesnon-hermitianrealalgebrasassociated
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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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