It is well-known that tunneling rates can be calculated through imaginary-time techniques: To leading order, the exponent of the tunneling rate is determined by the euclidean action of so-called instanton solutions. Despite the great importance of these results, it was only recently attempted to obtain a more general, non-perturbative understanding of these results using path integrals. Most importantly in the context of my talk, it was suggested that the length of the imaginary-time interval on which the instanton is defined is related to the physical time of the tunneling through a Wick-rotation. As the latter can be argued to be significantly larger than the typical dynamical time scale of the system of interest, this reproduces the familiar leading order results for tunneling out of a false vacuum.

This identification obviously fails for tunneling out of excited states, for which results obtained through the WKB method suggest that the instanton be defined on a finite euclidean-time interval. In my talk, I will explain how this tension can be resolved through the introduction of a new formalism, which can be understood as a real-time version of the familiar instanton-picture. After reviewing some relevant concepts of the existing literature I will introduce the most important concepts of this new formulation and demonstrate how they can be used to calculate tunneling rates at NLO for tunneling out of arbitrary initial states. This includes, in particular, the calculation of vacuum decay/bubble nucleation rates in realistic systems with finite temperature and time-dependent backgrounds.