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
This publication has 6 references indexed in Scilit:
- Expansion of a Function of Noncommuting OperatorsJournal of Mathematical Physics, 1965
- The formal power series for logexeyDuke Mathematical Journal, 1956
- On the exponential solution of differential equations for a linear operatorCommunications on Pure and Applied Mathematics, 1954
- Mathematical aspects of the quantum theory of fields. Part V. Fields modified by linear homogeneous forcesCommunications on Pure and Applied Mathematics, 1953
- Die linearen Beziehungen zwischen höheren KommutatorenMathematische Zeitschrift, 1948
- Über Invarianten in Lie'schen RingenMathematische Annalen, 1947