Robert Mann - An Introduction to Particle Physics and the Standard Model · Problem 9

Particle Classification — Robert Mann

Physics — Particle Physics · matrix-exponentials-commutators

Problem

For matrices

\mathbf{A}

and

\mathbf{B}

, show

\exp[-\mathbf{A}]\, \mathbf{B} \exp \mathbf{A} = \exp(-ad_{\mathbf{A}})\mathbf{B} \quad \text{where} \quad ad_{\mathbf{A}}\mathbf{B} \equiv [\mathbf{A}, \mathbf{B}]