The pre-Lie structure of the time-ordered exponential
arXiv:1305.3856 · doi:10.1007/s11005-014-0703-4
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.
References in corpus (1)
Cited by in corpus (9)
- Cumulants, free cumulants and half-shuffles
- Flows and stochastic Taylor series in Ito calculus
- On expansions for nonlinear systems, error estimates and convergence issues
- Post-symmetric braces and integration of post-Lie algebras
- From iterated integrals and chronological calculus to Hopf and Rota-Baxter algebras
- Shuffle group laws. Applications in free probability
- The combinatorics of Green's functions in planar field theories
- Cumulant-cumulant relations in free probability theory from Magnus' expansion
- What is the Magnus Expansion?