Properties of Higher-Order Commutator Products and the Baker-Hausdorff Formula
- 1 May 1968
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 9 (5) , 790-796
- https://doi.org/10.1063/1.1664643
Abstract
The element z = log exey , which is known to be an element of the Lie‐algebra generated by x and y, is expressed as a commutator series in x and y with coefficients given in terms of certain fixed polynomials. The result is given explicitly to sixth order. Useful recurrence relations are obtained. The method is based on certain properties of higher‐order commutator products, particularly their idempotent character.Keywords
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