|
| related topics |
| {vol, operators, histories} |
| {equation, function, exp} |
| {classical, space, random} |
| {state, states, coherent} |
| {temperature, thermal, energy} |
| {let, theorem, proof} |
| {operator, operators, space} |
| {bell, inequality, local} |
|
Normal Order: Combinatorial Graphs
Allan I. Solomon, Gerard Duchamp, Pawel Blasiak, Andrzej Horzela, Karol A. Penson
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0402082
- categories:
- quant-ph math.CO
- comments:
- 7 pages, 15 references, 2 figures. Presented at "Progress in
Supersymmetric Quantum Mechanics" (PSQM'03), Valladolid, Spain, July 2003
- arxiv_id:
- quant-ph/0402082
- created:
- 2004-02-12
Full article ▸
|
|
| related documents |
| 0107071v1 |
| 0311033v1 |
| 0412024v1 |
| 0412083v1 |
| 0605132v1 |
| 0605213v2 |
| 0407120v1 |
| 0406146v1 |
| 0507024v1 |
| 0507194v1 |
| 0612033v1 |
| 0606242v3 |
| 0502144v1 |
| 0703193v2 |
| 0406121v1 |
| 0701198v1 |
| 0501093v1 |
| 0507218v1 |
| 0402088v1 |
| 0603155v1 |
| 0610251v1 |
| 0701079v1 |
| 0608211v2 |
| 0403188v1 |
| 0507119v1 |
|