Time-Ordered Products and Exponentials
C.S. Lam (McGill University)
TL;DR
This paper presents a formula that decomposes time-ordered products into sums of commutator integrals, enabling explicit calculation of time-ordered exponentials and unifying several known formulas.
Contribution
It introduces a general decomposition formula for time-ordered products, generalizing the Campbell-Baker-Hausdorff and nonabelian eikonal formulas.
Findings
Derived an explicit formula for time-ordered exponentials.
Unified existing formulas as special cases.
Facilitated summation of infinite series in operator calculus.
Abstract
I discuss a formula decomposing the integral of time-ordered products of operators into sums of products of integrals of time-ordered commutators. The resulting factorization enables summation of an infinite series to be carried out to yield an explicit formula for the time-ordered exponentials. The Campbell-Baker-Hausdorff formula and the nonabelian eikonal formula obtained previously are both special cases of this result.
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Taxonomy
TopicsMatrix Theory and Algorithms