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Combinatorial algebra for second-quantized Quantum Theory

Blasiak, Pawel; Duchamp, Gerard H.E.; Solomon, Allan I.; Horzela, Andrzej and Penson, Karol A. (2010). Combinatorial algebra for second-quantized Quantum Theory. Advances in Theoretical and Mathematical Physics, 14(4) pp. 1209–1243.

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Abstract

We describe an algebra G of diagrams that faithfully gives a diagrammatic representation of the structures of both the Heisenberg–Weyl algebra H – the associative algebra of the creation and annihilation operators of quantum mechanics – and U(LH), the enveloping algebra of the Heisenberg Lie algebra LH. We show explicitly how G may be endowed with the structure of a Hopf algebra, which is also mirrored in the structure of U(LH). While both H and U(LH) are images of G, the algebra G has a richer structure and therefore embodies a finer combinatorial realization of the creation–annihilation system, of which it provides a concrete model.

Item Type: Journal Article
Copyright Holders: 2011 International Press
ISSN: 1095-0753
Academic Unit/Department: Science > Physical Sciences
Science
Item ID: 29285
Depositing User: Astrid Peterkin
Date Deposited: 22 Aug 2011 10:26
Last Modified: 25 Feb 2016 05:55
URI: http://oro.open.ac.uk/id/eprint/29285
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