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.