dorsal/arxiv
View SchemaNormal Order: Combinatorial Graphs
| Authors | Allan I. Solomon, Gerard Duchamp, Pawel Blasiak, Andrzej Horzela, Karol A. Penson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0402082 |
| URL | https://arxiv.org/abs/quant-ph/0402082 |
| DOI | 10.1142/9789812702340_0046 |
Abstract
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.
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"abstract": "A conventional context for supersymmetric problems arises when we consider\nsystems containing both boson and fermion operators. In this note we consider\nthe normal ordering problem for a string of such operators. In the general\ncase, upon which we touch briefly, this problem leads to combinatorial numbers,\nthe so-called Rook numbers. Since we assume that the two species, bosons and\nfermions, commute, we subsequently restrict ourselves to consideration of a\nsingle species, single-mode boson monomials. This problem leads to elegant\ngeneralisations of well-known combinatorial numbers, specifically Bell and\nStirling numbers. We explicitly give the generating functions for some classes\nof these numbers. In this note we concentrate on the combinatorial graph\napproach, showing how some important classical results of graph theory lead to\ntransparent representations of the combinatorial numbers associated with the\nboson normal ordering problem.",
"arxiv_id": "quant-ph/0402082",
"authors": [
"Allan I. Solomon",
"Gerard Duchamp",
"Pawel Blasiak",
"Andrzej Horzela",
"Karol A. Penson"
],
"categories": [
"quant-ph",
"math.CO"
],
"doi": "10.1142/9789812702340_0046",
"title": "Normal Order: Combinatorial Graphs",
"url": "https://arxiv.org/abs/quant-ph/0402082"
},
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