110 citations · 705 across the 38 of their papers we have counts for
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Parasupersymmetry and N-fold Supersymmetry in Quantum Many-Body Systems II. Third Order
Toshiaki Tanaka
Based on the general formalism of parafermionic algebra and parasupersymmetry proposed previously by us, we explicitly construct third-order parafermionic algebra and multiplicatio…
N-fold Parasupersymmetry
Toshiaki Tanaka
We find a new type of non-linear supersymmetries, called N-fold parasupersymmetry, which is a generalization of both N-fold supersymmetry and parasupersymmetry. We provide a genera…
Parasupersymmetry and N-fold Supersymmetry in Quantum Many-Body Systems I. General Formalism and Second Order
Toshiaki Tanaka
We propose an elegant formulation of parafermionic algebra and parasupersymmetry of arbitrary order in quantum many-body systems without recourse to any specific matrix representat…
General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space
Toshiaki Tanaka
In our previous work, we proposed a mathematical framework for PT-symmetric quantum theory, and in particular constructed a Krein space in which PT-symmetric operators would natura…
Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
Artemio Gonzalez-Lopez, Toshiaki Tanaka
We recall the importance of recognizing the different mathematical nature of various concepts relating to PT-symmetric quantum theories. After clarifying the relation between super…
On Existence of a Biorthonormal Basis Composed of Eigenvectors of Non-Hermitian Operators
Toshiaki Tanaka
We present a set of necessary conditions for the existence of a biorthonormal basis composed of eigenvectors of non-Hermitian operators. As an illustration, we examine these condit…
PT-Symmetric Quantum Theory Defined in a Krein Space
Toshiaki Tanaka
We provide a mathematical framework for PT-symmetric quantum theory, which is applicable irrespective of whether a system is defined on R or a complex contour, whether PT symmetry…