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We review the production of the matter-antimatter asymmetry in the earlyUniverse, that is baryogenesis, in out-of-equlibrium conditions induced bydecays of heavy particles or by the presence of phase boundaries. The mostprominent examples are given by leptogenesis and electroweak baryogenesis,respectively. For both cases, we derive the equations that govern theproduction of the asymmetries. We first use intuitive arguments based onclassical fluid equations in combination with quantum-field-theoretical effectsof CP-violation. As for a more thorough approach that is well-suited forsystematic improvements, we obtain the real-time evolution of the system ofinterest using the closed time-path method. We thus provide a simple andpracticable scheme to set up phenomenological fluid equations based on firstprinciples of quantum field theory. Necessary for baryogenesis are both, CPeven as well as odd phases in the amplitudes. A possibility of generating theeven phases is the coherent superposition of quantum states, i.e. mixing. Thesecoherence effects are essential in resonant leptogenesis as well as in somescenarios of electroweak baryogenesis. Recent theoretical progress onasymmetries from out-of-equlibrium decays may therefore also be applicable tobaryogenesis at phase boundaries.

Why is there more matter than antimatter? Calculational methods for leptogenesis and electroweak baryogenesis