We have searched for new physics beyond the Standard Model of elementary particle physics in dielectron decay mode at the CDF (Collider Detector at Fermilab) experiment in ppbar collisions at 1.96 TeV. The data were collected during the 2002-2003 runs corresponding to an integrated luminosity of 200 pb^-1. Many extensions of the Standard Model have been proposed. Grand Unified Theories (GUT) assumes a larger gauge symmetry group and predict new gauge bosons. GUT has the hierarchy problem in it and there have been many attempts to solve the hierarchy problem. Solutions for the hierarchy problem are supersymmetry, technicolor, large extra dimensions, warped extra dimensions and little Higgs models. We analyze the differential distribution of dielectron events in terms of their invariant mass and no significant excess is found in very high mass region. We present a 95% confidence level limit on the production cross section times branching ratio for new resonant particles decaying into an electron pair as a function of invariant mass. New resonant particles include new neutral gauge boson Z', Randall-Sundrum graviton, R-parity violating sneutrino, and technicolor particles. We also present limits on the effective Planck scale of large extra dimensions. Posted to /cdf/pub/thesis/cdf7487_ikado_thesis.ps http://www-cdf.fnal.gov/thesis/cdf7487_ikado_thesis.ps Posted by ikado@fcdfwww