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Ladder operators and endomorphisms in combinatorial Physics

By Gerard H. E. Duchamp, Laurent Poinsot, Allan I. Solomon, Karol A. Penson, Pawel Blasiak and Andrzej Horzela

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 <i>row-finite</i>, 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

Year: 2010
OAI identifier: oai:oro.open.ac.uk:22207
Provided by: Open Research Online

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