The pre-Lie structure of the time-ordered exponential
Rings and Algebras
2015-03-17 v1
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.
Keywords
Cite
@article{arxiv.1305.3856,
title = {The pre-Lie structure of the time-ordered exponential},
author = {Kurusch Ebrahimi-Fard and Frederic Patras},
journal= {arXiv preprint arXiv:1305.3856},
year = {2015}
}