Time-Ordering and a Generalized Magnus Expansion

Abstract : 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.
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Michel Bauer, Raphael Chetrite, Kurusch Ebrahimi-Fard, Frédéric Patras. Time-Ordering and a Generalized Magnus Expansion. Lett Math Phys, 2012, pp.Pas encore connu. 〈10.1007/s11005-012-0596-z〉. 〈hal-00762255〉

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