相关论文: Harmonic potentials for symmetric quaternionic sig…
$\mathcal{PT}$-symmetry --- invariance with respect to combined space reflection $\mathcal{P}$ and time reversal $\mathcal{T}$ --- provides a weaker condition than (Dirac) Hermiticity for ensuring a real energy spectrum of a general…
This paper is a short summary of already submitted papers hep-th/0410242 and hep-th/0502231. It provides a self contained description of earlier obtained results for physicists with traditional mathematical background.
A variational and perturbative treatment is provided for a family of generalized spiked harmonic oscillator Hamiltonians H = -(d/dx)^2 + B x^2 + A/x^2 + lambda/x^alpha, where B > 0, A >= 0, and alpha and lambda denote two real positive…
The scalar field theory with potential $V(\varphi)=\textstyle{\frac{1}{2}} m^2\varphi^2-\textstyle{\frac{1}{4}} g\varphi^4$ ($g>0$) is ill defined as a Hermitian theory but in a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric framework it…
A harmonic oscillator Hamiltonian augmented by a non-Hermitian \pt-symmetric part and its su(1,1) generalizations, for which a family of positive-definite metric operators was recently constructed, are re-examined in a supersymmetric…
A real potential Hamiltonian has real energy bound states below the scattering threshold and complex energy resonances above it. Scattering states are not square integrable, being instead delta function normalized. This lack of square…
The existence of bi-Hamiltonian structures for the rational Harmonic Oscillator (non-central harmonic oscillator with rational ratio of frequencies) is analyzed by making use of the geometric theory of symmetries. We prove that these…
We consider the semiclassical Schr\"odinger operator $-h^2\partial_x^2+V(x)$ on a half-line, where $V$ is a compactly supported potential which is positive near the endpoint of its support. We prove that the eigenvalues and the purely…
An integrable model for SU($\nu$) electrons with inverse-square interaction is studied for the system with confining harmonic potential. We develop a new description of the spectrum based on the {\it renormalized harmonic-oscillators} which…
Many aspects of pluripotential theory are generalized to quaternionic $m$-subharmonic functions. We introduce quaternionic version of notions of the $m$-Hessian operator, $m$-subharmonic functions, $m$-Hessian measure, $m$-capapcity, the…
We introduce hermiticity as a new symmetry and show that when starting with a model which is Hermitian in the classical level, quantum corrections can break hermiticity while the theory stay physically acceptable. To show this, we…
We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The…
We demonstrate that large class of PT-symmetric complex potentials, which can have isospectral real partner potentials, possess two different superpotentials. In the parameter domain, where the superpotential is unique, the spectrum is real…
We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, P\"oschl-Teller I and P\"oschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special…
We derive the complete set of continuous maximal symmetries for Standard Model (SM) alignment that may occur in the tree-level scalar potential of multi-Higgs Doublet Models, with $n > 2$ Higgs doublets. Our results generalize the…
We compute the relevant parameters of the combined Higgs and \phi scalar effective potential in the Littlest Higgs (LH) model. These parameters are obtained as the sum of two kind of contributions. The first one is the one-loop radiative…
We construct a superpotential for the general N=1/2 supersymmetric gauge theory coupled to chiral matter in the fundamental and adjoint representations, and investigate the one-loop renormalisability of the theories.
We derive the energy levels associated with the even-parity wave functions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical…
The higher order supersymmetric partners of a stationary periodic potential are studied. The transformation functions associated to the band edges do not change the spectral structure. However, when the transformation is implemented for…
It is known that the standard and the inverted harmonic oscillator are different. Replacing thus of {\omega} by i{\omega} in the regular oscillator is necessary going to give the inverted oscillator H^{r}. This replacement would lead to…