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The background is calculation of the little group elements of Poincare group for massless particles. I start with a bunch of exponentials of operators, and the end goal is to crunch them into the exponential of a single operator.

I simplified them to the product of three exponentials $e^A e^B e^C$ with seemingly no more interesting properties than that $[A,C]$ is proportional to $B$. Is it possible to further simplify this without resorting to the complicated Baker–Campbell–Hausdorff formula?

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