Tests of quantum electrodynamics with two-, three-, and four-photon final states from e+e- annihilation at sqrt s =29 GeV.

High-precision measurements of electron-positron annihilation into final states of two, three, and four photons are presented. The data were obtained with the MAC detector at the PEP storage ring of the Stanford Linear Accelerator Center, at a center-of-mass energy of 29 GeV. The measured ${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma} differential cross section is used to test the validity of quantum electrodynamics (QED) in this energy range; it agrees well with QED, and the limit on cutoff parameters for the electron propagator is \ensuremath{\Lambda}g66 GeV. The measurement of ${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma} is used to test the QED calculations of order ${\ensuremath{\alpha}}^{3}$ and to search for anomalies that would indicate the existence of new particles; the agreement with QED is excellent and no anomalies are found. Two events from the reaction ${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma} are found, in agreement with the QED prediction.