The Open UniversitySkip to content

Normal order: combinatorial graphs

Solomon, Allan I.; Duchamp, Gerard; Blasiak, Pawel; Horzela, Andrzej and Penson, Karol A. (2003). Normal order: combinatorial graphs. In: Progress in Supersymmetric Quantum Mechanics (PSQM'03), Jul 2003, Valladolid, Spain.

Google Scholar: Look up in Google Scholar


A conventional context for supersymmetric problems arises when we consider systems containing both boson and fermion operators. In this note we consider the normal ordering problem for a string of such operators. In the general case, upon which we touch briefly, this problem leads to combinatorial numbers, the so-called Rook numbers. Since we assume that the two species, bosons and fermions, commute, we subsequently restrict ourselves to consideration of a single species, single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, specifically Bell and Stirling numbers. We explicitly give the generating functions for some classes of these numbers. In this note we concentrate on the combinatorial graph approach, showing how some important classical results of graph theory lead to transparent representations of the combinatorial numbers associated with the boson normal ordering problem.

Item Type: Conference or Workshop Item
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Physical Sciences
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 4893
Depositing User: Users 6041 not found.
Date Deposited: 14 Jul 2006
Last Modified: 04 Oct 2016 09:53
Share this page:

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU