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.

DOI: https://doi.org/10.4310/atmp.2010.v14.n4.a5

URL: http://www.intlpress.com/ATMP/ATMP-issue_14_4.php

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.

Viewing alternatives

Look up in Google Scholar

Download history

Metrics

Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions

Item Actions

Export

About

CORE (COnnecting REpositories)

Recommendations