The speaker will present a semiclassical framework for determining the scaling dimensions of composite operators in conformal and quantum field theories. The main example will be the λϕ4 theory. The speaker will show how to obtain the full spectrum of composite operators built out of n fields transforming in the traceless-symmetric Lorentz representations to the next-to-leading order in the double-scaling limit n→∞, λ→0 with λn fixed. At any given order, the semiclassical expansion resums an infinite number of Feynman diagrams providing a systematic path to predict higher order terms in the traditional perturbative loop expansion.