|
This article is cited in 2 scientific papers (total in 2 papers)
Exponential Formulas, Normal Ordering and the Weyl–Heisenberg Algebra
Stjepan Meljanaca, Rina Štrajnb a Division of Theoretical Physics, Ruder Bošković Institute,
Bijenička cesta 54, 10002 Zagreb, Croatia
b Department of Electrical Engineering and Computing, University of Dubrovnik, Ćira Carića 4, 20000 Dubrovnik, Croatia
Abstract:
We consider a class of exponentials in the Weyl–Heisenberg algebra with exponents of type at most linear in coordinates and arbitrary functions of momenta. They are expressed in terms of normal ordering where coordinates stand to the left from momenta. Exponents appearing in normal ordered form satisfy differential equations with boundary conditions that could be solved perturbatively order by order. Two propositions are presented for the Weyl–Heisenberg algebra in 2 dimensions and their generalizations in higher dimensions. These results can be applied to arbitrary noncommutative spaces for construction of star products, coproducts of momenta and twist operators. They can also be related to the BCH formula.
Keywords:
exponential operators, normal ordering, Weyl–Heisenberg algebra, noncommutative geometry.
Received: May 27, 2021; in final form September 9, 2021; Published online September 15, 2021
Citation:
Stjepan Meljanac, Rina Štrajn, “Exponential Formulas, Normal Ordering and the Weyl–Heisenberg Algebra”, SIGMA, 17 (2021), 084, 7 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1766 https://www.mathnet.ru/eng/sigma/v17/p84
|
Statistics & downloads: |
Abstract page: | 51 | Full-text PDF : | 14 | References: | 8 |
|