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• Derivative_of_the_exponential_map abstract "In the theory of Lie groups, the exponential map is a map from the Lie algebra g of a Lie group G into G. In case G is a matrix Lie group, the exponential map reduces to the matrix exponential. The exponential map, denoted exp:g → G, is analytic and has as such a derivative d/dtexp(X(t)):Tg → TG, where X(t) is a C1 path in the Lie algebra, and a closely related differential dexp:Tg → TG.The formula for dexp was first proved by Friedrich Schur (1891). It was later elaborated by Henri Poincaré (1899) in the context of the problem of expressing Lie group multiplication using Lie algebraic terms. It is also sometimes known as Duhamel's formula.The formula is important both in pure and applied mathematics. It enters into proofs of theorems such as the Baker–Campbell–Hausdorff formula, and it is used frequently in physics for example in quantum field theory, as in the Magnus expansion in perturbation theory, and in lattice gauge theory.Throughout, the notations exp(X) and eX will be used interchangeably to denote the exponential given an argument, except when, where as noted, the notations have dedicated distinct meanings. The calculus-style notation is preferred here for better readability in equations. On the other hand, the exp-style is sometimes more convenient for inline equations, and is necessary on the rare occasions when there is a real distinction to be made.".
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• Derivative_of_the_exponential_map wikiPageWikiLink Adjoint_representation.
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• Derivative_of_the_exponential_map wikiPageWikiLink Analytic_manifold.
• Derivative_of_the_exponential_map wikiPageWikiLink Baker–Campbell–Hausdorff_formula.
• Derivative_of_the_exponential_map wikiPageWikiLink Category:Exponentials.
• Derivative_of_the_exponential_map wikiPageWikiLink Category:Lie_groups.
• Derivative_of_the_exponential_map wikiPageWikiLink Category:Mathematical_physics.
• Derivative_of_the_exponential_map wikiPageWikiLink Category:Matrix_theory.
• Derivative_of_the_exponential_map wikiPageWikiLink Derivative.
• Derivative_of_the_exponential_map wikiPageWikiLink Differential_of_a_function.
• Derivative_of_the_exponential_map wikiPageWikiLink Exponential_map_(Lie_theory).
• Derivative_of_the_exponential_map wikiPageWikiLink Flow_(mathematics).
• Derivative_of_the_exponential_map wikiPageWikiLink Friedrich_Schur.
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• Derivative_of_the_exponential_map wikiPageWikiLink Lattice_gauge_theory.
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• Derivative_of_the_exponential_map wikiPageWikiLink Logarithm_of_a_matrix.
• Derivative_of_the_exponential_map wikiPageWikiLink Magnus_expansion.
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• Derivative_of_the_exponential_map wikiPageWikiLink Mercator_series.
• Derivative_of_the_exponential_map wikiPageWikiLink Path_(topology).
• Derivative_of_the_exponential_map wikiPageWikiLink Perturbation_theory.
• Derivative_of_the_exponential_map wikiPageWikiLink Proceedings_of_the_USSR_Academy_of_Sciences.
• Derivative_of_the_exponential_map wikiPageWikiLink Quantum_field_theory.
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• Derivative_of_the_exponential_map wikiPageWikiLinkText "Derivative of the exponential map".
• Derivative_of_the_exponential_map wikiPageWikiLinkText "Poincaré−Hausdorff".
• Derivative_of_the_exponential_map wikiPageWikiLinkText "derivative of the exponential map".
• Derivative_of_the_exponential_map wikiPageWikiLinkText "here".
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• Derivative_of_the_exponential_map title "A direct formal approach".
• Derivative_of_the_exponential_map title "Combinatoric details".
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• Derivative_of_the_exponential_map subject Category:Exponentials.
• Derivative_of_the_exponential_map subject Category:Lie_groups.
• Derivative_of_the_exponential_map subject Category:Mathematical_physics.
• Derivative_of_the_exponential_map subject Category:Matrix_theory.
• Derivative_of_the_exponential_map hypernym Map.
• Derivative_of_the_exponential_map type Software.
• Derivative_of_the_exponential_map comment "In the theory of Lie groups, the exponential map is a map from the Lie algebra g of a Lie group G into G. In case G is a matrix Lie group, the exponential map reduces to the matrix exponential. The exponential map, denoted exp:g → G, is analytic and has as such a derivative d/dtexp(X(t)):Tg → TG, where X(t) is a C1 path in the Lie algebra, and a closely related differential dexp:Tg → TG.The formula for dexp was first proved by Friedrich Schur (1891).".
• Derivative_of_the_exponential_map label "Derivative of the exponential map".
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• Derivative_of_the_exponential_map depiction Poincare.jpg.
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