[en] In 2011, the Compact Muon Solenoid (CMS) detector recorded 5 fb^-1 of pp collision data delivered by the Large Hadron Collider at a centre-of-mass energy of 7 TeV. The large number of events from t anti t production allows to precisely analyse the production and decay of t anti t pairs in an unprecedented energy regime. In this thesis, the invariant mass distribution of the reconstructed t anti t system (m_tantit) is measured and compared to predictions according to the Standard Model of particle physics. With the help of the measured m_tantit distribution, searches for new particles decaying to a t anti t pair are performed. Such new particles would appear as resonant contributions in addition to the non-resonant m_tantit distributions from Standard Model background processes. The focus of the data analysis extends from invariant top quark pair masses near the production threshold of m_tantit∝2 m(top) to the region of m(t anti t)∝2 TeV. The analysis is based on the final state of the t anti t system with one charged lepton, i.e. either a muon or an electron, a neutrino, and four jets, of which two are b quark jets. A full kinematic reconstruction of these events is performed with a χ² method. The selected events are divided in 8 subsamples according to the number of selected jets, the number of jets that are identified as b quark jets, and the lepton flavour (muon or electron). This categorisation takes advantage of the different signal-to-background ratios in the different event categories and improves the statistical sensitivity of the search. The measured m_tantit distributions in all 8 subsamples show good agreement with the expectation from the background processes that are simulated according to the Standard Model. The compatibility is tested by performing a background-only fit including all relevant systematic uncertainties. Stringent limits are set on the production cross section for new particles that are predicted by a number of models for new physics. The considered masses extend from 0.5 TeV to 2 TeV, with the corresponding expected cross section limits at 95% confidence level ranging from 3 pb to 0.2 pb for a Z' model with a width that is small compared to the m(t anti t) resolution. A leptophobic topcolour Z' with a width of 1.2% (10%) of its mass is excluded for m (Z')<1.33 TeV (m(Z')<1.72 TeV) at 95% confidence level. In addition, a Kaluza-Klein gluon in a Randall-Sundrum model is excluded with a mass up to m(g')=1.45 TeV. The upper limits can also be interpreted in a model-independent way and improve the limits on the production cross section for narrow-width Z'-like particle set by the CDF and D0 collaborations as well as by the ATLAS collaboration in a large part of the considered mass range.