Quantum kinematics on q-deformed quantum spaces I, Mathematical Framework
量子物理
2007-05-23 v1
摘要
The aim of these two papers (I and II) is to try to give fundamental concepts of quantum kinematics to q-deformed quantum spaces. Paper I introduces the relevant mathematical concepts. A short review of the basic ideas of q-deformed analysis is given. These considerations are continued by introducing q-deformed analogs of Fourier transformations and delta functions. Their properties are discussed in detail. Furthermore, q-deformed versions of sesquilinear forms are defined, their basic properties are derived, and q-analogs of the Fourier-Plancherel identity are proved. In paper II these reasonings are applied to wave functions on position and momentum space.
引用
@article{arxiv.quant-ph/0612173,
title = {Quantum kinematics on q-deformed quantum spaces I, Mathematical Framework},
author = {Hartmut Wachter},
journal= {arXiv preprint arXiv:quant-ph/0612173},
year = {2007}
}