Related papers: SUSY-hierarchy of one-dimensional reflectionless p…
We consider noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY Yang-Mills theory. We show that one-loop renormalizability of noncommutative scalar electrodynamics requires the scalar potential to be an anticommutator squared.…
If supersymmetry (SUSY) exists in nature and is a solution to the hierarchy problem then it should be detectable at the TeV energy scale which the large hadron collider (LHC) is now exploring. One of the main goals of the LHC is the…
Broken-supersymmetry is used to define a reflectionless active cavity capable of amplifying electromagnetic radiation in the visible. The approach is analytical through the use of the Darboux transform for the generation of the optical…
Supersymmetry (SUSY) helps solve the hierarchy problem in high-energy physics and provides a natural groundwork for unifying gravity with other fundamental interactions. While being one of the most promising frameworks for theories beyond…
We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible…
Modifications of the authors' previously-published, generalized, lumped-element, reflectionless filter topologies are presented which remove the original constraints on the relative values of its prototype parameters. Thus, any transfer…
We propose a novel class of $\mathcal{N}=1$ supergravity (called ``Relaxed supergravity'') that can enlarge the space of scalar potentials, relaxing the strongly-constrained form of the prototype supergravity potential. It has very long…
A mirror that reflects light fully and yet is transparent appears paradoxical. Current so-called transparent or "one-way" mirrors are not perfectly reflective and thus can be distinguished from a standard mirror. Constructing a transparent…
Originally developed in the context of quantum field theory, the concept of supersymmetry (SUSY) can be used to systematically design a new class of optical structures. In this work, we demonstrate how key features arising from optical…
We construct a pseudoclassical particle model associated to the twisted N=2 SUSY algebra in four dimensions. The particle model has four kappa symmetries. Three of them can be used to reduce the model to the vector supersymmetry particle…
This paper provides an overview of supersymmetry (SUSY) and the ongoing efforts to detect SUSY particles at the Large Hadron Collider (LHC). SUSY proposes corresponding "sparticles" for each Standard Model particle, with the potential to…
The aim of this paper is to provide the mathematical framework for analyzing the possibility of rendering one dimensional objects visible with difficulty and ultimately invisible,by changing the experimental conditions to which they are…
A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second order symmetries, is considered. After separation of variables, the one-dimensional matrix…
The development of supersymmetric (SUSY) quantum mechanics has shown that some of the insights based on the algebraic properties of ladder operators related to the quantum mechanical harmonic oscillator carry over to the study of more…
Spectral properties of a coupled $N \times N$ potential model obtained with the help of a single non-conservative supersymmetric (SUSY) transformation starting from a system of $N$ radial Schr\"odinger equations with the zero potential and…
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives the intertwined Hamiltonians correspond to…
Pairs of SUSY partner Hamiltonians are studied which are interrelated by usual (linear) or polynomial supersymmetry. Assuming the model of one of the Hamiltonians as exactly solvable with known propagator, expressions for propagators of…
A second shape invariance property of the two-dimensional generalized Morse potential is discovered. Though the potential is not amenable to conventional separation of variables, the above property allows to build purely algebraically part…
Two new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations…
Rigid SUSY with gauge symmetry has a simple form for the Higgs potential. It is the positive semi--definite sum of the squares of the auxiliary fields. Setting the potential to zero yields a set of equations for the Vacuum Expectation…