Ladder operators and endomorphisms in combinatorial Physics

Duchamp, Gerard H. E.; Poinsot, Laurent; Solomon, Allan I.; Penson, Karol A.; Blasiak, Pawel and Horzela, Andrzej (2010). Ladder operators and endomorphisms in combinatorial Physics. Discrete Mathematics & Theoretical Computer Science, 12(2) pp. 23–46.

URL: http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/art...

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 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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