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- Q804316 subject Q7013402.
- Q804316 subject Q7020692.
- Q804316 subject Q7457477.
- Q804316 subject Q8805755.
- Q804316 abstract "In mathematics, the Baker–Campbell–Hausdorff formula is the solution to Z = log(eX eY)for possibly noncommutative X and Y in the Lie algebra of a Lie group. This formula tightly links Lie groups to Lie algebras by expressing the logarithm of the product of two Lie group elements as a Lie algebra element using only Lie algebraic operations. The solution on this form, whenever defined, means that multiplication in the group can be expressed entirely in Lie algebraic terms. The solution on another form is straightforward to obtain; one just substitutes the power series for exp and log in the equation and rearranges. The point is to express the solution in Lie algebraic terms. This occupied the time of several prominent mathematicians.The formula is named after Henry Frederick Baker, John Edward Campbell, and Felix Hausdorff who discovered its qualitative form, i.e. that only commutators and commutators of commutators, ad infinitum, are needed to express the solution. This qualitative form is what is used in the most important applications, such as the relatively accessible proofs of the Lie correspondence and in quantum field theory. It was first noted in print by Campbell (1897); elaborated by Henri Poincaré (1899) and Baker (1902); and systematized geometrically, and linked to the Jacobi identity by Hausdorff (1906). The first actual explicit formula, with all numerical coefficients, is due to Eugene Dynkin (1947).".
- Q804316 wikiPageExternalLink lie_algebras.pdf.
- Q804316 wikiPageExternalLink Baker-Campbell-HausdorffSeries.html.
- Q804316 wikiPageExternalLink S0273-0979-1982-14972-2.pdf.
- Q804316 wikiPageExternalLink CBH.pdf.
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- Q804316 comment "In mathematics, the Baker–Campbell–Hausdorff formula is the solution to Z = log(eX eY)for possibly noncommutative X and Y in the Lie algebra of a Lie group. This formula tightly links Lie groups to Lie algebras by expressing the logarithm of the product of two Lie group elements as a Lie algebra element using only Lie algebraic operations. The solution on this form, whenever defined, means that multiplication in the group can be expressed entirely in Lie algebraic terms.".
- Q804316 label "Baker–Campbell–Hausdorff formula".