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Open Quantum Systems Decoherence Quantum Foundations

Combinatorics and Boson normal ordering: A gentle introduction

arXiv

Authors: P. Blasiak, A. Horzela, K. A. Penson, A. I. Solomon, G. H. E. Duchamp

Year

2007

Paper ID

50497

Status

Preprint

Abstract Read

~2 min

Abstract Words

Citations

N/A

Abstract

We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling numbers enumerating partitions of a set. This framework reveals several inherent relations between ordering problems and combinatorial objects, and displays the analytical background to Wick's theorem. The methodology can be straightforwardly generalized from the simple example given herein to a wide class of operators.

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We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0704.3116 [2] arXiv https://arxiv.org/abs/0704.3116 [3] Publisher https://arxiv.org/abs/0704.3116

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