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.
Liste complète des métadonnées

Cited literature [26 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00762255
Contributor : Raphael Chetrite <>
Submitted on : Friday, December 7, 2012 - 4:24:11 PM
Last modification on : Thursday, February 7, 2019 - 4:19:34 PM
Document(s) archivé(s) le : Friday, March 8, 2013 - 3:50:48 AM

File

BauerChetriteFardPatras.pdf
Files produced by the author(s)

Identifiers

Citation

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⟩

Share

Metrics

Record views

425

Files downloads

730