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On a Z_3-Graded Generalization of the Witten Index
Ali Mostafazadeh
We construct a realization of the algebra of the Z_3-graded topological symmetry of type (1,1,1) in terms of a pair of operators D_1: H_1 -> H_2, and D_2: H_2 -> H_3 satisfying [D_…
On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry
Ali Mostafazadeh
We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations…
Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
Ali Mostafazadeh
We give a necessary and sufficient condition for the reality of the spectrum of a non-Hermitian Hamiltonian admitting a complete set of biorthonormal eigenvectors.
On the Dynamical Invariants and the Geometric Phases for a General Spin System in a Changing Magnetic Field
Ali Mostafazadeh
We consider a class of general spin Hamiltonians of the form where and describe the dipole interaction of the spins with an arbitrary time-de…
Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
Ali Mostafazadeh
We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamilto…
Variational Sturmian Approximation: A nonperturbative method of solving time-independent Schrödinger equation
Ali Mostafazadeh
A variationally improved Sturmian approximation for solving time-independent Schrödinger equation is developed. This approximation is used to obtain the energy levels of a quartic…
On the Statistical Origin of Topological Symmetries
K. Aghababaei Samani, A. Mostafazadeh
We investigate a quantum system possessing a parasupersymmetry of order 2, an orthosupersymmetry of order , a fractional supersymmetry of order , and topological symmetries…
Supersymmetric Dynamical Invariants
Ali Mostafazadeh
We address the problem of identifying the (nonstationary) quantum systems that admit supersymmetric dynamical invariants. In particular, we give a general expression for the bosoni…
Cosmological Adiabatic Geometric Phase of a Scalar Field in a Bianchi Spacetime
A. Mostafazadeh
A two-component formulation of the Klein-Gordon equation is used to investigate the cyclic and noncyclic adiabatic geometric phases due to spatially homogeneous (Bianchi) cosmologi…
Geometric Phases, Symmetries of Dynamical Invariants, and Exact Solution of the Schrödinger Equation
Ali Mostafazadeh
We introduce the notion of the geometrically equivalent quantum systems (GEQS) as quantum systems that lead to the same geometric phases for a given complete set of initial state v…