Ladder Operators and Endomorphisms in Combinatorial Physics

Details Ladder Operators and Endomorphisms in Combinatorial Physics Ladder Operators and Endomorphisms in Combinatorial Physics

2009-08-17

arxiv.org/abs/0908.2332v2

DMTCS 12, 2 (2010) 1

Mathematics

Combinatorics

Scientific paper

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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