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\(\text{sl}(2, \mathbb C)\) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues. (English) Zbl 1050.81546

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

MSC:

81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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