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We describe the construction of quantum gates (unitary operators) from boolean functions and give a number of applications. Both non-reversible and reversible boolean functions are considered. The construction of the Hamilton operator for a…
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…
The variety of ideas put forward in the context of a "composite" picture for the Higgs boson calls for a simple and effective description of the related phenomenology. Such a description is given here by means of a "minimal" model and is…
We construct creation and annihilation operators for harmonic oscillators with minimal length uncertainty relations. We discuss a possible generalization to a large class of deformations of cannonical commutation relations. We also discuss…
The operators that break supersymmetry can be holomorphic or non-holomorphic in structure. The latter do not pose any problem for gauge hierarchy and are soft provided that the particle spectrum does not contain any gauge singlets. In…
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or $q$-boson algebra which…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of…
An introduction to spin techniques in particle physics is given. Among the topics covered are: helicity formalism and its applications to the decay and scattering of spin-1/2 and spin-1 particles, techniques for evaluating helicity…
We review how the rho meson can be modeled in an effective theory and discuss the implications of applying this approach to heavier spin-one resonances. Georgi's vector limit is explored, and its relationship to locality in a deconstructed…
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…
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…
I briefly review the physics of the Higgs sector in the Standard Model (SM) and its supersymmetric extension, in particular the MSSM, and discuss the prospects for discovering the Higgs particles at the Large Hadron Collider. Some emphasis…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
We analyse the properties of a strongly-damped quantum harmonic oscillator by means of an exact diagonalisation of the full Hamiltonian, including both the oscillator and the reservoir degrees of freedom to which it is coupled. Many of the…
It is shown that the quantum Hamiltonian characterising a non-relativistic electron under the influence of an external spherical symmetric electromagnetic potential exhibits a supersymmetric structure. Both cases, spherical symmetric scalar…
Various forms of the $q$-boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator. Both the one-component and the multicomponent $q$-bosons are discussed. As a byproduct, we obtain a new…
In this work, we describe certain pseudo-Hermitian extensions of the harmonic and isotonic oscillators, both of which are exactly-solvable models in quantum mechanics. By coupling the dynamics of a particle moving in a one-dimensional…
Higgs boson may serve as a portal to new physics beyond the standard model (BSM) which is implied by theoretical naturalness or experimental anomalies. In this note we briefly survey some Higgs-related BSM physics models, including the low…
The dynamical algebra of the q-deformed harmonic oscillator is constructed. As a result, we find the free deformed Hamiltonian as well as the Hamiltonian of the deformed oscillator as a complicated, momentum dependent interaction…