| Summary: | The top quark is the heaviest fundamental particle. Its correspondingly short lifetime implies that it will decay before top flavoured hadrons can form. This provides an opportunity to study the properties of a quark without the effects of hadronisation, which is unique in the standard model.Using data recorded by the D0 experiment at the Fermilab Tevatron collider, and corresponding to \unit[5.4]{fb^{-1}} of proton-antiproton collisions two analyses of the production and decay mechanism of top quarks are presented in this thesis. In the standard model the directions of the spin of top quarks produced in pairs by the strong interaction are expected to be correlated. In the first analysis, the strength of the correlation is extracted from the angles of the two leptons in the top quark and antiquark rest frames, yielding a correlation strength C=0.10\pm0.45. This is in agreement with the NLO QCD prediction within two standard deviations, but also in agreement with the no correlation hypothesis.In the second analysis, forward-backward asymmetries in top quark-antiquark production are measured using the charged leptons from top quark decays. We find that the angular distributions of \ell^{\mathrm{-}} relative to antiprotons and \ell^{+} relative to protons are in agreement with each other. Combining the two distributions and correcting for detector acceptance we obtain the forward-backward asymmetry \al=\left(5.8\pm5.1\mathrm{(stat)}\pm1.3\mathrm{(syst)}\right)\%, compared to the standard model prediction of \al\mathrm{(predicted)}=\left(4.7\pm0.1\right)\%.
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