Study of multiphoton final states and tests of QED in e$^+$e$^-$ collisions at $\sqrt s$ up to 209 GeV

The process e+ e- -> n gamma with n =2 is studied at centre-of-mass energies ranging from \root(s)=192 to 208 GeV. The data sample corresponds to a total integrated luminosity of 427 1/pb. The total and differential cross sections are found to be in agreement with the QED expectations. Using all the data collected with the L3 detector above the Z pole, limits on deviations from QED, excited electrons, contact interactions, extra space dimensions and excited spin-3/2 leptons are set.