Krawtchouk matrices from the Feynman path integral and from the split quaternions
Abstract
An interpretation of Krawtchouk matrices in terms of discrete version of the Feynman path integral is given. Also, an algebraic characterization in terms of the algebra of split quaternions is provided. The resulting properties include an easy inference of the spectral decomposition. It is also an occasion for an expository clarification of the role of Krawtchouk matrices in different areas, including quantum information.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 DOI:
 10.48550/arXiv.1604.00109
 arXiv:
 arXiv:1604.00109
 Bibcode:
 2016arXiv160400109K
 Keywords:

 Mathematics  Group Theory;
 Mathematical Physics;
 60G50;
 47A80;
 81P99;
 46L53;
 81R05
 EPrint:
 37 pages, 16 figures