Solomon, A. I.; Duchamp, G. H. E.; Blasiak, P.; Horzela, A. and Penson, K. A.
(2011).
*Journal of Physics: Conference Series*, 284 012055.

URL: | http://dx.doi.org/10.1088/1742-6596/284/1/012055 |
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Google Scholar: | Look up in Google Scholar |

## Abstract

We show that the combinatorial numbers known as *Bell numbers* are generic in quantum physics. This is because they arise in the procedure known as *Normal ordering* of bosons, a procedure which is involved in the evaluation of quantum functions such as the canonical partition function of quantum statistical physics, *inter alia.* In fact, we shall show that an evaluation of the non-interacting partition function for a single boson system is identical to integrating the *exponential generating function* of the Bell numbers, which is a device for encapsulating a combinatorial sequence in a single function.

We then introduce a remarkable equality, the Dobinski relation, and use it to indicate why renormalisation is necessary in even the simplest of perturbation expansions for a partition function.

Finally we introduce a global algebraic description of this simple model, giving a Hopf algebra, which provides a starting point for extensions to more complex physical systems.

Item Type: | Article |
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Copyright Holders: | IOP Publishing |

ISSN: | 1742-6588 |

Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Physical Sciences Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 28712 |

Depositing User: | Astrid Peterkin |

Date Deposited: | 09 May 2011 08:47 |

Last Modified: | 06 Oct 2016 17:38 |

URI: | http://oro.open.ac.uk/id/eprint/28712 |

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