55956853
Minimal areas from q-deformed oscillator algebras
On the basis of various examples we provide evidence that noncommutative spacetime involving position-dependent structure constants will give rise to deformed oscillator algebras. In turn, starting from some q-deformations of these algebras in a two-dimensional space for which the entire deformed Fock space can be constructed explicitly, we derive the commutation relations for the dynamical variables in noncommutative spacetime. We compute minimal areas resulting from these relations, i.e. finitely extended regions for which it is impossible to resolve any substructure in form of measurable knowledge. The size of the regions we find is determined by the noncommutative constant and the deformation parameter q. Any object in this type of spacetime structure has to be of membrane type or in certain limits of string type.
118783546
Masslessness of the up quark and eta-->3pi0 decay
18319013
Non-Hermitian Hamiltonians with real and complex eigenvalues: An sl(2,C) approach
Potential algebras are extended from Hermitian to non-Hermitian Hamiltonians and shown to provide an elegant method for studying the transition from real to complex eigenvalues for a class of non-Hermitian Hamiltonians associated with the complex Lie algebra A$_1$.
18633717
CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C
A brief overview is given of recent developments and fresh ideas at the intersection of - and/or -symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). Within the framework of the resulting supersymmetric version of -symmetric quantum mechanics we study the consequences of the assumption that the "charge" operator is represented in a differential-operator form of the second or higher order. Besides the freedom allowed by the Hermiticity constraint for the operator , encouraging results are obtained in the second-order case. In particular, the integrability of intertwining relations proves to match the closure of our nonlinear (viz., polynomial) SUSY algebra. In a particular illustration, our form of -symmetric SUSY QM leads to a new class of non-Hermitian polynomial oscillators with real spectrum which turn out to be -asymmetric.
16287686
PT-symmetric sextic potentials
Abstract The family of complex PT-symmetric sextic potentials is studied to show that for various cases the system is essentially quasi-solvable and possesses real, discrete energy eigenvalues. For a particular choice of parameters, we find that under supersymmetric transformations the underlying potential picks up a reflectionless part.
124385266
Mixing angles and decay constants of eta, eta-prime and eta(c)
120952330
The Zero-Energy Continuum Bound State of the Saito Potential
122334428
Integral equations and the bound‐state problem
An integral equation for the s‐wave bound‐state solution is derived and then solved for a square‐well potential. It is shown that the scattering solutions continue to exist at negative energies, and when evaluated at the energy of a bound state these solutions do reduce to the bound‐state solution. The bound‐state energies of a square‐well potential are deduced also from orthogonality considerations. Finally, the existence of bound states for an arbitrary short‐range potential is related to the occurrence of zeros of the Jost function or poles of the S matrix for that potential.