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 (947kB)
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 Item
Copyright Holders: 2011 International Press
ISSN: 1095-0753
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Physical Sciences
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 29285
Depositing User: Astrid Peterkin
Date Deposited: 22 Aug 2011 10:26
Last Modified: 09 Feb 2018 05:45
Share this page:

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU