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The pre-Lie structure of the time-ordered exponential

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.

preprint2013arXivOpen access
Kurusch Ebrahimi-FardFrederic Patras
math.RA
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Open access2 authors1 topic
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Kurusch Ebrahimi-FardFrederic Patras

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