Razpadna širina lažnega vakuuma skalarnega polja na eni zanki

This thesis explores the false vacuum decay rate of a scalar field at one-loop order in two, three, and four dimensions using semiclassical methods. The results are compared with established analytical solutions in the thin-wall limit, where the true and false vacua are nearly degenerate. A central element of this work is the bounce solution, which describes the most probable tunneling path between the false and true vacua, along with its associated Euclidean action. The action is renormalized to eliminate divergences in even dimensions, and the renormalization group running is examined. The contribution of quantum fluctuations around the bounce solution, expressed as a ratio of functional determinants, is analyzed and determined using the Gel'fand-Yaglom theorem. As part of this approach, the zero eigenvalues are systematically removed. The ratio of functional determinants is renormalized, providing a finite result for the decay rate. This result is consistent with the thin-wall approximation and remains valid until the false vacuum transitions into an inflection point.