The effective mass approximation is widely used across models of carrier transport, optical response, and excitons in semiconductors and insulators, but its validity hinges on the assumption that the band dispersion $E_n\left(\mathbf{k}\right)$ at the relevant extremum is analytic. We prove that analyticity holds at any nondegenerate extremum for Kohn-Sham density functional theory (DFT) with local or hybrid exchange-correlation functionals, for Hartree-Fock, and for band-edge $G_0{W}_0$ quasiparticle energies in gapped systems. Band nonanalyticity (or warping) in these settings is therefore intrinsically tied to degeneracy. We then use group theory to determine the symmetry-allowed form of the effective mass tensor for each of the 32 crystallographic point groups, providing a stringent consistency check on first-principles calculations. As a representative application, we show that the electron and hole effective masses at the $K$ point of monolayer ${\mathrm{MoS}}_2$ must be strictly isotropic at the DFT and $G_0{W}_0$ levels.

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• Band gap
• Dielectric properties
• Electronic structure
• Density functional theory
• Effective mass theory
• First-principles calculations
• Functional analytical methods
• GW method