Combinatorics of boson normal ordering and some applications
arXiv:quant-ph/0507206
Abstract
We provide the solution to the normal ordering problem for powers and exponentials of two classes of operators. The first one consists of boson strings and more generally homogeneous polynomials, while the second one treats operators linear in one of the creation or annihilation operators. Both solutions generalize Bell and Stirling numbers arising in the number operator case. We use the advanced combinatorial analysis to provide closed form expressions, generating functions, recurrences, etc. The analysis is based on the Dobiński-type relations and the umbral calculus methods. As an illustration of this framework we point out the applications to the construction of generalized coherent states, operator calculus and ordering of deformed bosons.
PhD Thesis: University of Paris VI and Polish Academy of Sciences, Krakow, Poland (103 pages, 7 figures, 82 references)
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Cited by in corpus (11)
- Combinatorics and Boson normal ordering: A gentle introduction
- Some identities on degenerate r-stirling numbers via boson operators
- A generalization of boson normal ordering
- Back-reaction in strong field QED: a toy model
- Normally ordered forms of powers of differential operators and their combinatorics
- Monomiality principle, Sheffer-type polynomials and the normal ordering problem
- Noncrossing normal ordering for functions of boson operators
- Hiking a generalized Dyck path: A tractable way of calculating multimode boson evolution operators
- Generalized Stirling Numbers I
- Generalized -Stirling numbers and normal ordering
- A combinatorial Hopf algebra for the boson normal ordering problem