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We present a new criterion, based on commutator methods, for the strongmixing property of unitary representations of topological groups equipped witha proper length function. Our result generalises and unifies recent results onthe strong mixing property of discrete flows $\{U^N\}_{N\in\mathbb Z}$ andcontinuous flows $\{{\rm e}^{-itH}\}_{t\in\mathbb R}$ induced by unitaryoperators $U$ and self-adjoint operators $H$ in a Hilbert space. As anapplication, we present a short alternative proof (not using convolutions) ofthe strong mixing property of the left regular representation of$\sigma$-compact locally compact groups.

Commutator criteria for strong mixing II. More general and simpler