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arXiv · 0908.2332

Ladder Operators and Endomorphisms in Combinatorial Physics

Gérard Henry Edmond Duchamp·Laurent Poinsot·Allan I. Solomon·Karol A. Penson·Pawel Blasiak·Andrzej Horzela
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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 $\C[[x]]$. 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.

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Gérard Henry Edmond Duchamp, Laurent Poinsot, Allan I. Solomon, Karol A. Penson, Pawel Blasiak, Andrzej Horzela. 2009-08-17. Ladder Operators and Endomorphisms in Combinatorial Physics. https://arxiv.org/abs/0908.2332

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