q-deformed Fourier Theory
| dc.creator | Schwenk, J. | |
| dc.date | 1994-06-24 | |
| dc.date | 1994-07-15 | |
| dc.date.accessioned | 2026-07-07T09:03:41Z | |
| dc.date.available | 2026-07-07T09:03:41Z | |
| dc.description | We solve the problem of Fourier transformation for the one-dimensional $q$-deformed Heisenberg algebra. Starting from a matrix representation of this algebra we observe that momentum and position are unbounded operators in the Hilbert space. Therefore, in order to diagonalise the position operator in a momentum eigenbasis we have to study self-adjoint extensions of these operators. It turns out that there exist a whole family of such extensions for the position operator. This leads, correspondingly, to a one-parametric family of Fourier transformations. These transformations, which are related to continued fractions, are constructed in terms of $q$-deformed trigonometric functions. The entire family of the Fourier transformations turns out to be characterised by an elliptic function. | |
| dc.description | 19, MPI-PhT/94-36 (14.July 1994) | |
| dc.identifier | https://arxiv.org/abs/hep-th/9406168 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9406168 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149106 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | q-deformed Fourier Theory | |
| dc.type | text |