The Pre-Lie Structure of the Time-Ordered Exponential

2013/05/16 by Kurusch Ebrahimi-Fard, Frédéric Patras, Frederic Patras · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.RA

paper · pdf · doi:10.1007/s11005-014-0703-4

published as Letters in Mathematical Physics, Volume 104, Issue 10, (2014) 1281-1302

arxiv created 2013/05/16 · openalex publication_date 2014/07/01 · arxiv updated 2015/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02

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.

Citations

• On the exponential solution of differential equations for a linear operator
• A Magnus- and Fer-Type Formula in Dendriform Algebras
• Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

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