In mathematics, the Lie product formula, named for Sophus Lie (1875), but also widely called the Trotter product formula,[1] named after Hale Trotter, states that for arbitrary m × m real or complex matrices A and B,[2]
The Lie–Trotter product formula[3] and the Trotter–Kato theorem[4] extend this to certain unbounded linear operators A and B.
However, the Lie product formula holds for all matrices A and B, even ones which do not commute.
The formula has applications, for example, in the path integral formulation of quantum mechanics.
The same idea is used in the construction of splitting methods for the numerical solution of differential equations.
Moreover, the Lie product theorem is sufficient to prove the Feynman–Kac formula.
[7] By the Baker–Campbell–Hausdorff formula, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.")