‎We consider the oscillator group equipped with‎ ‎a biinvariant Lorentzian metric‎. ‎Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional‎ ‎restricted to vector fields‎. ‎Left-invariant vector fields defining harmonic maps are...

The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...

The fermionic oscillator defined by the algebraic relations cc∗ + c∗c = 1 and c = 0 admits the homogeneous group O(2) as its invariance group. We show that, the structure of the inhomogeneous invariance group of this oscillator is a quantum group. Quantum field theory which describes the ultimate behavior of elementary particles and fields in physics fundamentally depends on the concepts of the...