Momentum transforms and Laplacians in fractional spaces
Mathematical Physics
2015-03-20 v3 High Energy Physics - Theory
math.MP
Abstract
We define an infinite class of unitary transformations between position and momentum fractional spaces, thus generalizing the Fourier transform to a special class of fractal geometries. Each transform diagonalizes a unique Laplacian operator. We also introduce a new version of fractional spaces, where coordinates and momenta span the whole real line. In one topological dimension, these results are extended to more general measures.
Keywords
Cite
@article{arxiv.1202.5383,
title = {Momentum transforms and Laplacians in fractional spaces},
author = {Gianluca Calcagni and Giuseppe Nardelli},
journal= {arXiv preprint arXiv:1202.5383},
year = {2015}
}
Comments
32 pages, 1 double figure. v2: conclusions extended; v3: minor typos corrected