110 citations · 705 across the 38 of their papers we have counts for
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Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry II. The N=3 Case
Bijan Bagchi, Toshiaki Tanaka
We continue the previous study on the existence of different intermediate Hamiltonians in type A N-fold supersymmetric systems and carry out an exhaustive investigation on the N=3…
Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry
Bijan Bagchi, Toshiaki Tanaka
Type A N-fold supercharge admits a one-parameter family of factorizations into product of N first-order linear differential operators due to an underlying GL(2,C) symmetry. As a co…
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…
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…
Simultaneous Ordinary and Type A N-fold Supersymmetries in Schroedinger, Pauli, and Dirac Equations
Choon-Lin Ho, Toshiaki Tanaka
We investigate physical models which possess simultaneous ordinary and type A N-fold supersymmetries, which we call type A (N,1)-fold supersymmetry. Inequivalent type A (N,1)-fold…
Simultaneous Type A N-fold Supersymmetry with Two Different Values of N
Choon-Lin Ho, Toshiaki Tanaka
We investigate one-dimensional quantum mechanical systems which have type A N-fold supersymmetry with two different values of N simultaneously. We find that there are essentially f…
A New Construction of Quasi-solvable Quantum Many-body Systems of Deformed Calogero-Sutherland Type
Toshiaki Tanaka
We make a new multivariate generalization of the type A monomial space of a single variable. It is different from the previously introduced type A space of several variables which…
A Many-body Generalization of Quasi-solvable Models with Type C N-fold Supersymmetry (I) Regular Cases
Toshiaki Tanaka
We make a generalization of the type C monomial space of a single variable, which was introduced in the construction of type C N-fold supersymmetry, to several variables. Then, we…
A Novel Multi-parameter Family of Quantum Systems with Partially Broken N-fold Supersymmetry
Artemio Gonzalez-Lopez, Toshiaki Tanaka
We develop a systematic algorithm for constructing an N-fold supersymmetric system from a given vector space invariant under one of the supercharges. Applying this algorithm to spa…
A New Family of N-fold Supersymmetry: Type B
Artemio Gonzalez-Lopez, Toshiaki Tanaka
We construct a new family of N-fold supersymmetric systems which is referred to as ``type B''. A higher derivative representation of the N-fold supercharge for this new family is g…
sl(M+1) Construction of Quasi-solvable Quantum M-body Systems
Toshiaki Tanaka
We propose a systematic method to construct quasi-solvable quantum many-body systems having permutation symmetry. By the introduction of elementary symmetric polynomials and suitab…
Type A N-fold Supersymmetry and Generalized Bender-Dunne Polynomials
Toshiaki Tanaka
We derive the necessary and sufficient condition for Type A N-fold supersymmetry by direct calculation of the intertwining relation and show the complete equivalence between this a…
Nonperturbative Aspects in N-fold Supersymmetry
Toshiaki Tanaka, Masatoshi Sato
Through a nonperturbative analysis on a sextic triple-well potential, we reveal novel aspects of the dynamical property of the system in connection with N-fold supersymmetry and qu…
A Family of Quasi-solvable Quantum Many-body Systems
Toshiaki Tanaka
We construct a family of quasi-solvable quantum many-body systems by an algebraic method. The models contain up to two-body interactions and have permutation symmetry. We classify…
N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -
Masatoshi Sato, Toshiaki Tanaka
We investigate particular models which can be N-fold supersymmetric at specific values of a parameter in the Hamiltonians. The models to be investigated are a periodic potential an…
Classification of Type A N-fold supersymmetry
Hideaki Aoyama, Noriko Nakayama, Masatoshi Sato +1
Type A N-fold supersymmetry of one-dimensional quantum mechanics can be constructed by using sl(2) generators represented on a finite dimensional functional space. Using this sl(2)…
sl(2) Construction of Type A N-fold supersymmetry
Hideaki Aoyama, Noriko Nakayama, Masatoshi Sato +1
N-fold supersymmetry is an extension of the ordinary supersymmetry in one-dimensional quantum mechanics. One of its major property is quasi-solvability, which means that energy eig…