The Open UniversitySkip to content

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.

Full text available as:
PDF (Accepted Manuscript) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (925Kb)
Google Scholar: Look up in Google Scholar


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
Item ID: 29285
Depositing User: Astrid Peterkin
Date Deposited: 22 Aug 2011 10:26
Last Modified: 25 Jan 2016 10:35
Share this page:

Actions (login may be required)

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340