This thesis describes a search for new heavy particles decaying into electron-positron pairs. The search utilizes 1.08 inverse femtobarn of proton-proton collisions at a center-of-mass energy of sqrt(s) = 7 TeV, produced in 2011 by the Large Hadron Collider and recorded with the ATLAS detector at the CERN laboratory in Switzerland. The reconstructed dielectron invariant mass spectrum is compared to Standard Model expectations. Since no significant excess is found, upper limits on the cross-section times branching ratio of Z' bosons and Randall-Sundrum gravitons are determined at the 95% confidence level using a Bayesian approach. These limits are combined with limits obtained by a parallel analysis in the muon channel and converted into lower limits on the masses of the Sequential Standard Model Z' boson (1.88 TeV), E6 Z' bosons (1.54 - 1.68 TeV) as well as the Randall-Sundrum graviton (1.67 TeV for k/MPl = 0.1).
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