Computing the Baker–Campbell–Hausdorff series and the Zassenhaus product

Analytical evaluation of the numerical coefficients in the Zassenhaus product formula and its applications to quantum and statistical mechanics

“…In this section, we will study an analytical approach to determine the coefficients in the Zassenhaus exponents in front of the nested commutators. The knowledge of these coefficients inspired several recent works (see for example [28,29,30]). As we will see, the result will have several important applications.…”

Approximately disentangling exponential operators

“…13. Practical methods for the calculation of the coefficients ⌳ n s are reviewed and developed in Ref.…”

On multivariable Zassenhaus formula

“…where W k (X, Y ) is a homogeneous Lie polynomial in X and Y of degree k [4]. The first few terms are There are several methods to compute W k [5,6,7,8]. In particular, a recursive algorithm has been proposed in [9] to express directly W k with the minimum number of independent commutators required at each degree k. Similar to the BCH formula, the Zassenhaus formula is useful in many different fields: q-analysis in quantum groups [10], quantum nonlinear optics [13], the Schrödinger equation in the semiclassical regime [12], and splitting methods in numerical analysis [11], etc.…”