Search for new physics in final states with a high energy electron and large missing transverse energy

The most successful and comprehensive theory describing the microcosm is the Standard Model of particle physics (SM). It comprises all known elementary particles and describes in high precision the basic processes of three of the four fundamental interactions. But still, not all experimental observations and theoretical challenges are covered. Many models exist that take the SM as a good approximation of natural phenomena in already discovered energy regions, but extend it in various ways. The Large Hadron Collider (LHC) provides the opportunity to look into these high energy regions using proton-proton collisions at significantly higher center-of-mass energies than previous experiments. This dissertation searches for physics beyond the SM especially in final states with one highly energetic electron (respectively positron) and large missing transverse energy. With the data set recorded in 2012 by the ATLAS detector, a large multi-purpose detector making use of the LHC, the spectrum of the related combined transverse mass can be measured up to the TeV scale. To find any evidence to the existence of new physics beyond the SM, it was searched for significant deviations between the observed data and the expectations due to SM processes. Unfortunately, no significant excess could be observed and exclusion limits in the context of three different new physics scenarios are provided. Besides a so-called Sequential Standard Model (SSM) predicting additional vector gauge bosons, also the possible existence of (charged) chiral bosons is analyzed. Also inferences about dark matter candidates called ``weakly interacting massive particles (WIMP)'' are drawn. With the aid of a Bayesian ansatz, the observed (expected) exclusion limit on the boson pole mass is set to 3.13$\,$TeV (3.13$\,$TeV) for a SSM W$'$ boson and to 3.08$\,$TeV (3.08$\,$TeV) for charged chiral W$^*$ bosons (at 95$\,\%$ C.L.).