A Note on the Baker–Campbell–Hausdorff Series in Terms of Right-Nested Commutators

• Autores: Ana M. Arnal Pons , Fernando Casas Pérez , Cristina Chiralt Monleón
• Localización: Mediterranean journal of mathematics, ISSN 1660-5446, Vol. 18, Nº. 2, 2021
• Idioma: inglés
• DOI: 10.1007/s00009-020-01681-6
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• Resumen

  • We get compact expressions for the Baker–Campbell–Hausdorff series Z=log(eXeY) in terms of right-nested commutators. The reduction in the number of terms originates from two facts: (i) we use as a starting point an explicit expression directly involving independent commutators and (ii) we derive a complete set of identities arising among right-nested commutators. The procedure allows us to obtain the series with fewer terms than when expressed in the classical Hall basis at least up to terms of grade 10.