2012/06/18 by Michel Bauer, Raphaël Chétrite, Raphael Chetrite +4 · 15 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Applied mathematics #Context (archaeology) #Differential equation #Generalization #Geometry #Linear differential equation #Logarithm #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Operator (biology) #Product (mathematics) #Pure mathematics #math-ph #math.CA #math.CO #math.MP
paper · pdf · doi:10.1007/s11005-012-0596-z
published in Letters in Mathematical Physics 103(3), 331-350 (Springer Science+Business Media)
arxiv created 2012/06/18 · openalex publication_date 2012/11/23 · arxiv updated 2013/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in statistical physics, we introduce a generalization of the Magnus expansion. Whereas the classical expansion computes the logarithm of the evolution operator of a linear differential equation, our generalization addresses the same problem, including however directly a non-trivial initial condition. As a by-product we recover a variant of the time ordering operation, known as T*-ordering. Eventually, placing our results in the general context of Rota-Baxter algebras permits us to present them in a more natural algebraic setting. It encompasses, for example, the case where one considers linear difference equations instead of linear differential equations.