  We develop a novel renormalization approach for frustrated quantum
antiferromagnets. It is designed to consistently treat spin-wave interactions
all over the magnetic Brillouin zone, including high-energy modes in outer
regions as well as low energy modes in the center. Focusing on the paradigmatic
$J_1$-$J_2$ model, we find a unifying description of the second-order
transition between the N\'eel phase and the paramagnetic phase and the
first-order transition between the N\'eel phase and the columnar phase. Our
approach provides explicit results for the renormalized values of the spin
stiffness and spin-wave velocity characterizing the low-energy magnons in the
N\'eel phase.
