In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schrödinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the action of the unitary group on the Hilbert space allows to relate both approaches. We also study Weyl-Wigner approach to Quantum Mechanics and discuss the implica...

By considering 'coloured' braid group representation we have obtained a quantum group, which reduces to the standard GL q (2) and GL p,q (2) cases at some particular limits of the 'colour' parameters. In spite of quite complicated nature, all of these new quantum group relations can be expressed neatly in the Heisenberg-Weyl form, for a nontrivial choice of the basis elements. Furthermore, it i...

We define a three-parameter deformation of the Weyl-Heisenberg algebra that generalizes the q-oscillator algebra. By a purely algebraical procedure, we set up on this quantum space two differential calculi that are shown to be invariant on the same quantum group, extended to a ten-generator Hopf-star-algebra. We prove that, when the values of the parameters are related, the two differential cal...

We consider a class of exponentials in the Weyl-Heisenberg algebra with exponents type at most linear coordinates and arbitrary functions momenta. They are expressed terms normal ordering where stand to left from Exponents appearing ordered form satisfy differential equations boundary conditions that could be solved perturbatively order by order. Two propositions presented for 2 dimensions thei...

It is shown that the higher order supersymmetric partners of the harmonic oscillator Hamiltonian provide the simplest non-trivial realizations of the polynomial Heisenberg algebras. A linearized version of the corresponding annihilation and creation operator leads to a Fock representation which is the same as for the harmonic oscillator Hamiltonian. 1. Introduction. The non-linear algebras have...

Inspired by the work of A. Bonami and S. Poornima that a non-constant function which is homogeneous degree 0 cannot be Fourier multiplier on Sobolev spaces, we establish analogous results for multipliers Heisenberg group Hn Weyl Cn acting Spaces.