Related papers: No zero energy states for the supersymmetric x^2y^…
We discuss a formulation of harmonic superspace approach for noncommuative N=2 supersymmetric field theories paying main attention on new features arising because of noncommutativity. We begin with the known notions of the harmonic…
In this paper, we prove a form of the strong comparison principle for a class of fully nonlinear subelliptic operators of the form $\nabla^{2}_{H}\psi+L(\cdot,\psi,\nabla_{H}\psi)$ on the Heisenberg group, which include the CR invariant…
Matrix quasi exactly solvable operators are considered and new conditions are determined to test whether a matrix differential operator possesses one or several finite dimensional invariant vector spaces. New examples of $2\times 2$-matrix…
We exploit the ideas of spin-statistics theorem, normal-ordering and the key concepts behind the symmetry principles to derive the canonical (anti)commutators for the case of a one (0 + 1)-dimensional (1D) N = 2 supersymmetric (SUSY)…
The C operator in PT-symmetric quantum mechanics satisfies a system of three simultaneous algebraic operator equations, $C^2=1$, $[C,PT]=0$, and $[C,H]=0$. These equations are difficult to solve exactly, so perturbative methods have been…
Let $\mathcal{G}$ be a metric noncompact connected graph with finitely many edges. The main object of the paper is the Hamiltonian ${\bf H}_{\alpha}$ associated in $L^2(\mathcal{G};\mathbb{C}^m)$ with a matrix Sturm-Liouville expression and…
For the SU(N) invariant supersymmetric matrix model related to membranes in 4 space-time dimensions, the general solution to the equation(s) $Q^{\dagger}\Psi=0$ $(Q\chi =0)$ is determined for N odd. For any such (bosonic) solution of…
For the so-called source-probe configuration in Matrix theory, we prove the following theorem concerning the power of supersymmetry (SUSY): Let $\delta$ be a quantum-corrected effective SUSY transformation operator expandable in powers of…
We present a supersymmetric analysis of the wave problem with a Demkov-Ostrovsky spherically symmetric class of focusing potentials at zero energy. Following a suggestion of L\'evai, we work in the so-called R_0=0 sector in order to obtain…
In this paper, we give conditions forcing nilpotent matrices (and bounded linear operators in general) to be null or equivalently to be normal. Therefore, a non-zero operator having e.g. a positive real part is never nilpotent. The case of…
We revisit the moduli space approximation to the quantum mechanics of monopoles in N=4 supersymmetric Yang-Mills-Higgs theory with maximal symmetry breaking. Starting with the observation that the set of fermionic zero-modes in N=4…
We show that a symmetric informationally-complete positive operator-valued measure exists in a given dimension $d$ if and only if there exists a $d^2$-dimensional operator system satisfying certain order-theoretic conditions. We also…
Motivated by the concept of shape invariance in supersymmetric quantum mechanics, we obtain potentials whose spectrum consists of two shifted sets of equally spaced energy levels. These potentials are similar to the Calogero-Sutherland…
We prove a dispersive estimate for the evolution of Schroedinger operators $H = -\Delta + V(x)$ in ${\mathbb R}^3$. The potential is allowed to be a complex-valued function belonging to $L^p(\R^3)\cap L^q(\R^3)$, $p < \frac32 < q$, so that…
We revisit the novel symmetries in $\mathcal{N}$ = 2 supersymmetric (SUSY) quantum mechanical (QM) models by considering specific examples of coupled systems. Further, we extend our analysis to a general case and list out all the novel…
We prove a limiting absorption principle at zero energy for two-body Schr\"odinger operators with long-range potentials having a positive virial at infinity. More precisely, we establish a complete asymptotic expansion of the resolvent in…
We provide lower bounds for the sum of the negative eigenvalues of the operator $|\sigma\cdot p_A|^{2s} - C_s/|x|^{2s} + V$ in three dimensions, where $s\in (0, 1]$, covering the interesting physical cases $s = 1$ and $s = 1/2$. Here…
Some PT-symmetric non-hermitean Hamiltonians have only real eigenvalues. There is numerical evidence that the associated PT-invariant energy eigenstates satisfy an unconventional completeness relation. An ad hoc scalar product among the…
Some new characterizations of nonnegative Hamiltonian operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian operators to be invertible are obtained; so that the main results in the…
The goal of this paper is twofold. We prove that the operator $H=L+V$ , a perturbation of the Taibleson-Vladimirov multiplier $L=\mathfrak{D}^{\alpha}$ by a potential $V(x)=b\left\Vert x\right\Vert ^{-\alpha},$ $b\geq b_{\ast},$ is…