The pre-Lie structure of the time-ordered exponential

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.
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Contributor : Patras Frédéric <>
Submitted on : Thursday, September 26, 2013 - 5:52:08 PM
Last modification on : Friday, January 12, 2018 - 1:51:49 AM

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Kurusch Ebrahimi-Fard, Frederic Patras. The pre-Lie structure of the time-ordered exponential. Letters in Mathematical Physics, Springer Verlag, 2014, 104, pp.1281-1302. 〈10.1007/s11005-014-0703-4〉. 〈hal-00866614〉

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