16 research outputs found
All the Groups of Signal Analysis from the (1+1)-affine Galilei Group
We study the relationship between the (1+1)-affine Galilei group and four
groups of interest in signal analysis and image processing, viz., the wavelet
or the affine group of the line, the Weyl-Heisenberg, the shearlet and the
Stockwell groups. We show how all these groups can be obtained either directly
as subgroups, or as subgroups of central extensions of the affine Galilei
group. We also study this at the level of unitary representations of the groups
on Hilbert spaces.Comment: 28 pages, 1 figur
Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics
While Wigner functions forming phase space representation of quantum states is a well-known fact, their construction for noncommutative quantum mechanics (NCQM) remains relatively lesser known, in particular with respect to gauge dependencies. This paper deals with the construction of Wigner functions of NCQM for a system of 2-degrees of freedom using 2-parameter families of gauge equivalence classes of unitary irreducible representations (UIRs) of the Lie group G NC which has been identified as the kinematical symmetry group of NCQM in an earlier paper. This general construction of Wigner functions for NCQM, in turn, yields the special cases of Landau and symmetric gauges of NCQM