The Weyl-Heisenberg Group on the Noncommutative Two-Torus: A Zoo of Representations

A Necessary Condition for Weyl-Heisenberg Frames

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

Kronecker foliation, D1-branes and Morita equivalence of Noncommutative two-tori

It is known that the physics of open strings on a D2-brane on a two-torus is realized from the viewpoint of deformation quantization in the Seiberg-Witten limit. We study its T-dual theory, i.e. D1-brane physics on two-tori. Such theory is described by Kronecker foliation. The algebra of open strings on the D1-brane is then identified with the crossed product representation of a noncommutative ...

F eb 2 00 3 Representation of Semigroups in Rigged Hilbert Spaces : Subsemigroups of the Weyl - Heisenberg Group

This paper studies how differentiable representations of certain subsemigroups of the Weyl-Heisenberg group may be obtained in suitably constructed rigged Hilbert spaces. These semigroup representations are induced from a continuous unitary representation of the Weyl-Heisenberg group in a Hilbert space. Aspects of the rigged Hilbert space formulation of time asymmetric quantum mechanics are als...

An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups

Many exponential speedups that have been achieved in quantum computing are obtained via hidden subgroup problems (HSPs). We show that the HSP over Weyl-Heisenberg groups can be solved efficiently on a quantum computer. These groups are well-known in physics and play an important role in the theory of quantum error-correcting codes. Our algorithm is based on noncommutative Fourier analysis of co...