4,407 research outputs found
Classical quasi-trigonometric matrices of Cremmer-Gervais type and their quantization
We propose a method of quantization of certain Lie bialgebra structures on
the polynomial Lie algebras related to quasi-trigonometric solutions of the
classical Yang-Baxter equation. The method is based on so-called affinization
of certain seaweed algebras and their quantum analogues.Comment: 9 pages, LaTe
SUSY transformations with complex factorization constants. Application to spectral singularities
Supersymmetric (SUSY) transformation operators corresponding to complex
factorization constants are analyzed as operators acting in the Hilbert space
of functions square integrable on the positive semiaxis. Obtained results are
applied to Hamiltonians possessing spectral singularities which are
non-Hermitian SUSY partners of selfadjoint operators. A new regularization
procedure for the resolution of the identity operator in terms of continuous
biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed.
It is also shown that the continuous spectrum eigenfunction has zero binorm (in
the sense of distributions) at the singular point.Comment: Thanks to A. Sokolov a number of inaccuracies are correcte
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