Ladder Operators and Endomorphisms in Combinatorial Physics
Combinatorics
2010-11-04 v2 Symbolic Computation
Quantum Physics
Abstract
Starting with the Heisenberg-Weyl algebra, fundamental to quantum physics, we first show how the ordering of the non-commuting operators intrinsic to that algebra gives rise to generalizations of the classical Stirling Numbers of Combinatorics. These may be expressed in terms of infinite, but {\em row-finite}, matrices, which may also be considered as endomorphisms of . This leads us to consider endomorphisms in more general spaces, and these in turn may be expressed in terms of generalizations of the ladder-operators familiar in physics.
Cite
@article{arxiv.0908.2332,
title = {Ladder Operators and Endomorphisms in Combinatorial Physics},
author = {Gérard Henry Edmond Duchamp and Laurent Poinsot and Allan I. Solomon and Karol A. Penson and Pawel Blasiak and Andrzej Horzela},
journal= {arXiv preprint arXiv:0908.2332},
year = {2010}
}