Letters in Mathematical Physics

, Volume 104, Issue 10, pp 1281–1302

The Pre-Lie Structure of the Time-Ordered Exponential

Article

Abstract

The usual time-ordering operation and the corresponding time-ordered exponential play a fundamental role in physics and applied mathematics. In this work, we study a new approach to the understanding of time-ordering relying on recent progress made in the context of enveloping algebras of pre-Lie algebras. Various general formulas for pre-Lie and Rota–Baxter algebras are obtained in the process. Among others, we recover the noncommutative analog of the classical Bohnenblust–Spitzer formula, and get explicit formulae for operator products of time-ordered exponentials.

Mathematics Subject Classification (2010)

05E15 16T05 16T30 

Keywords

pre-Lie algebra time-ordering time-ordered exponential Rota–Baxter algebra Grossman–Larson algebra Bohnenblust–Spitzer identity Baker–Campbell–Hausdorff formula 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.ICMATMadridSpain
  2. 2.Univ. de Nice, Labo. J.-A. Dieudonné, UMR 7351, CNRSNice Cedex 02France

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