Quantum phase transitions in topological Josephson junctions

In this thesis, we extend the theoretical models for topological Josephson systems by including the dynamics of bosonic fields which couple to one-dimensional Majorana modes propagating along the junction. In our analysis of the resulting field theories, we find evidence for the existence of a variety of quantum phase transitions. Furthermore, we establish a regime in which the frequently used effective description in terms of two counter-propagating Majorana modes is no longer applicable due to an emergence of additional low-energy degrees of freedom, previously overlooked.