Overview of the Heisenberg–Weyl Algebra and Subsets of Riordan Subgroups

Overview on Heisenberg - Weyl Algebra and Subsets of Riordan Subgroups

In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg–Weyl, its Bargmann–Fock representation with differential operators and the associated one-parameter group. Upon this basis, the paper is then devoted to the groups of Riordan matrices associated to the related transformations of matrices (i.e. substitutions with prefun...

A Necessary Condition for Weyl-Heisenberg Frames

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

Heisenberg–Weyl algebra revisited: Combinatorics of words and paths

The Heisenberg–Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a lattice with some decomposition rules. We also discuss the rook problem on the associated Ferrers board; this is related to the calculus in the normally ordered basis. From thi...

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 ...