During the last decades, particle physicists have studied the tiniest building blocks of matter--the quarks and the leptons--and the forces between them in great detail. From these experiments, a theoretical framework has been built that describes the observed results with high precision. The achievement of this theory, which is referred to as the Standard Model of elementary particle physics, was the elaboration of a unified description of the strong, weak and electromagnetic forces in the framework of quantum gauge-field theories. Moreover, the Standard Model combines the weak and electromagnetic forces in a single electroweak gauge theory. The fourth force which is realized in nature, gravity, is too weak to be observable in laboratory experiments carried out in high-energy particle physics and is not part of the Standard Model. Although the Standard Model has proven highly successful in correlating a huge amount of experimental results, a key ingredient is as yet untested: the origin of electroweak symmetry breaking. Currently, the only viable ansatz that is compatible with observation is the Higgs mechanism. It predicts the existence of a scalar particle, called the Higgs boson, and the couplings to the fundamental Standard Model particles, however not its mass. An upper limit on the mass of the Higgs boson of {approx} 1 TeV can be inferred from unitarity arguments. One of the key tasks of particle physics in the next years will be to verify the existence of this particle. The introduction of an elementary scalar particle in a quantum field theory is highly problematic. The Higgs boson mass is subject to large quantum corrections, which makes it difficult to understand how its mass can be less than a TeV as required by theory. In addition, the Standard Model does not provide an answer to fundamental questions like the values of free parameters of the model, the pending integration of gravity or the evolution of the coupling constants of the fundamental forces at large energy regimes. Hence there are strong reasons to believe that the Standard Model is only a low-energy approximation to a more fundamental theory. One of the best studied candidates for an extension of the Standard Model is supersymmetry, which predicts the existence of a supersymmetric partner for each fundamental particle that differs only in spin. To allow different masses for Standard Model particles and their corresponding supersymmetric partners, supersymmetry must be broken. The mechanism behind supersymmetry breaking is currently unknown, however, various hypotheses exist. Supersymmetric models do not only solve the problem of the large quantum corrections to the Higgs boson mass, but they also allow the unification of the coupling constants at a common scale. In addition, certain supersymmetric models provide a suitable candidate for cold dark matter, which represents a large fraction of mass in our universe. Searches for supersymmetric particles have been performed by the four LEP experiments (ALEPH, DELPHI, L3, OPAL) up to the kinematic limit. Since no evidence for supersymmetric particles has been found, lower limits on their masses have been derived. The search for supersymmetry is now continuing at the Tevatron collider, located at the Fermi National Accelerator Laboratory in Batavia, Illinois. Two dedicated detector systems, CDF and D0, are installed at the Tevatron to analyze proton-antiproton collisions at a center-of-mass energy of 1.96 TeV. A particular promising discovery channel for supersymmetry within the Tevatron energy range is the trilepton channel. In this channel, the lighter supersymmetric partners of the Higgs and gauge bosons, the charginos and neutralinos, decay into final states with leptons or hadrons and missing energy. Using the leptonic final states, the signal can be separated from the large Standard Model background. Supersymmetry requires an extension of the Standard Model Higgs sector, leading to more than one neutral Higgs boson. Enhanced couplings result in sizable cross sections for Higgs boson production, and the decay into a tau pair becomes an important Higgs boson discovery channel. Within the present thesis, a search for new physics predicted by constrained supersymmetric models is performed in final states consisting of an electron and a tau using data collected with the D0 detector from April 2002 to July 2004. The first analysis searches for the associated production of the lightest chargino and the second lightest neutralino in final states with an electron, a hadronically decaying tau, an additional lepton and missing transverse energy: e + {tau}{sub h} + {ell} + E{sub T}. The second analysis searches for neutral supersymmetric Higgs bosons in the decay mode {phi} {yields} {tau}{tau} {yields} e + {tau}{sub h} + E{sub T}. To improve the sensitivity, the results are interpreted in combination with other channels.
