Solomon, A. I.; Blasiak, P.; Duchamp, G. E. H.; Horzela, A. and Penson, K. A.
(2004).

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Abstract
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the partition function, for example, is essentially a combinatorial problem. In this talk we shall show that one approach is via the normal ordering of the second quantized operators appearing in the partition function. This in turn leads to a combinatorial graphical description, giving essentially Feynman{type graphs associated with the theory. We illustrate this methodology by the explicit calculation of two model examples, the free boson gas and a super uid boson model. We show how the calculation of partition functions can be facilitated by knowledge of the combinatorics of the boson normal ordering problem; this naturally gives rise to the Bell numbers of combinatorics. The associated graphical representation of these numbers gives a perturbation expansion in terms of a sequence of graphs analogous to zero{dimensional Feynman diagrams. [brace not closed]
Item Type:  Conference or Workshop Item 

Copyright Holders:  2004 The Author 
Keywords:  boson normal ordering; combinatorics 
Academic Unit/School:  Faculty of Science, Technology, Engineering and Mathematics (STEM) > Physical Sciences Faculty of Science, Technology, Engineering and Mathematics (STEM) 
Item ID:  20814 
Depositing User:  Astrid Peterkin 
Date Deposited:  23 Mar 2010 10:49 
Last Modified:  08 Oct 2016 08:11 
URI:  http://oro.open.ac.uk/id/eprint/20814 
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