The Baker–Campbell–Hausdorff formula and nested commutator identities

DOI10.1063/1.529428zbMath0725.47052OpenAlexW1973616932MaRDI QIDQ5201829

José Angel Oteo

Publication date: 1991

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529428

zbMATH Keywords

Baker-Campbell-Hausdorff expansion

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Structure theory for Lie algebras and superalgebras (17B05) Commutators, derivations, elementary operators, etc. (47B47)

Related Items (23)

Consensus for formation control of multi-agent systems ⋮ A note on the Baker-Campbell-Hausdorff series in terms of right-nested commutators ⋮ Coordinated tracking for multiple nonholonomic vehicles on SE(2) ⋮ Goldberg's theorem and the Baker-Campbell-Hausdorff formula ⋮ Quantum variational principle and quantum multiform structure: the case of quadratic Lagrangians ⋮ Effective approximation for the semiclassical Schrödinger equation ⋮ Operator-splitting methods via the Zassenhaus product formula ⋮ The early proofs of the theorem of Campbell, Baker, Hausdorff, and Dynkin ⋮ Posetted trees and Baker-Campbell-Hausdorff product ⋮ Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields ⋮ Higher order operator splitting methods via Zassenhaus product formula: theory and applications ⋮ A simple expression for the terms in the Baker–Campbell–Hausdorff series ⋮ Variations on a theme of Jost and Pais ⋮ From time-ordered products to Magnus expansion ⋮ The joy and pain of skew symmetry ⋮ Multistep methods integrating ordinary differential equations on manifolds ⋮ Closed-form modified Hamiltonians for integrable numerical integration schemes ⋮ Maximal reductions in the Baker–Hausdorff formula ⋮ An efficient algorithm for computing the Baker–Campbell–Hausdorff series and some of its applications ⋮ On the convergence and optimization of the Baker-Campbell-Hausdorff formula ⋮ Exponential operators and the algebraic description of quantum confined systems ⋮ Approximately disentangling exponential operators ⋮ A note on the Zassenhaus product formula

Cites Work

• The formal power series for \(\log\,e^x e^y\)
• The Campbell-Baker-Hausdorff expansion for classical and quantum kicked dynamics
• On relations between commutators
• Dynkin’s method of computing the terms of the Baker–Campbell–Hausdorff series
• The Baker-Hausdorff Formula and a Problem in Crystal Physics
• Lie series and invariant functions for analytic symplectic maps
• The Baker-Campbell-Hausdorff formula and the convergence of the Magnus expansion
• Expansion of the Campbell‐Baker‐Hausdorff formula by computer
• Exponential Operators and Parameter Differentiation in Quantum Physics
• On the exponential solution of differential equations for a linear operator

This page was built for publication: The Baker–Campbell–Hausdorff formula and nested commutator identities