Heisenberg–Weyl algebra revisited: Combinatorics of words and paths

A Necessary Condition for Weyl-Heisenberg Frames

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Variations on a theme of Heisenberg, Pauli and Weyl1

The parentage between Weyl pairs, generalized Pauli group and unitary group is investigated in detail. We start from an abstract definition of the Heisenberg-Weyl group on the field R and then switch to the discrete Heisenberg-Weyl group or generalized Pauli group on a finite ring Zd. The main characteristics of the latter group, an abstract group of order d noted Pd, are given (conjugacy class...

q-oscillators, (non-)Kähler manifolds and constrained dynamics

It is shown that q-deformed quantummechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kähler manifolds, or as a quantum theory with second (or first)-class constraints. 1. The q-deformed Heisenberg-Weyl algebras [1], [2] exhibiting the quantum group symmetries [3],[4] have attracted much attention of physicists and mathema...

2 00 6 Un - equivalency Theorem between Deformed and undeformed Heisenberg - Weyl ’ s Algebras

Two fundamental issues about the relation between the deformed Heisenberg-Weyl algebra in noncommutative space and the undeformed one in commutative space are elucidated. First the un-equivalency theorem between two algebras is proved: the deformed algebra related to the undeformed one by a non-orthogonal similarity transformation is explored; furthermore, non-existence of a unitary similarity ...