Beliaev theory of spinor Bose-Einstein condensates

► Second-order energy spectra for a spin-1 87Rb spinor BEC under a quadratic Zeeman effect are found. ► Effective mass of magnons increases due to quantum fluctuations. ► Enhancement factor is the same for two quantum phases and also independent of external parameters. ► Lifetime of magnons in a spin-1 87Rb spinor BEC is much longer than that of phonons. ► Experimental scheme to measure the effective mass of magnons is proposed.