Tests of Quantum Electrodynamics and Electroweak Theory Using the Reactions Electron-Positron ---> Photon -

High statistics measurements of the differential cross sections for electron-positron annihilation into final states of 2, 3 and 4 photons (e('+)e('-) (--->) (gamma)(gamma)((gamma)((gamma)))) and electron-positron pair (e('+)e('-) (--->) e('+)e(' -)) are presented. The measurements were performed using the Magnetic Calorimeter detector (MAC) at the Positron Electron Project (PEP) of the Stanford Linear Accelerator Center (SLAC) at a center of mass energy of 29 GeV. The measurement of the e('+)e('-) (--->) (gamma)(gamma) cross section was used to test the validity of Quantum Electrodynamics (QED) in this energy range; the measurement agrees well with QED and the limits on cut-off parameters for the photon propagator are (LAMDA) > 66 GeV. The measurement of e('+)e(' -) (--->) (gamma)(gamma)(gamma) was used to test the QED calculations of order (alpha)('3) and to search for anomalies which would indicate new particles; the agreement with QED was excellent and no anomalies were found. Two events from the reaction e('+)e('-) (--->) (gamma)(gamma)(gamma)(gamma), an (alpha)('4) process, were found, representing the first observation of this rare final state. The measurement of the e('+)e('-) (--->) e('+)e('-) cross section (absolutely normalized using the e('+)e('-) (--->) (gamma)(gamma) data) was used to search for weak neutral current effects expected from the Electroweak gauge theory. A statistically significant deviation from pure QED was observed, giving the first evidence of weak neutral current effects in e('+)e('-) (--->) e('+)e('-). The weak couplings of the electron are measured to be (g(,a)('e))('2) = 0.33 (+OR-) 0.24 and (g(,v)('e))('2) = 0.09 (+OR-) 0.14.