We study the decay of false domain walls, which are metastable states of the quantum theory where the true vacuum is trapped inside the wall, with the false vacuum outside. We consider a theory with two scalar fields, a shepherd field and a field of
sheep. The shepherd field serves to herd the solitons of the sheep field so that they are nicely bunched together. However, quantum tunnelling of the shepherd field releases the sheep to spread out uncontrollably. We show how to calculate the tunnelling amplitude for such a disintegration.
Dynamical effects in general relativity have been finally, relatively recently observed by LIGOcite{2016LRR....19....1A}. To be able to measure these signals, great care has to be taken to minimize all sources of noise in the detector. One of the sou
rces of noise is called Newtonian noise. In this article we present an analysis of the dynamical (time dependent) nature of the Newtonian noise. In that respect, it is a misnomer to call it Newtonian noise, the Newtonian theory does not afford any dynamical notion of the gravitational field. The dynamical aspects of the nature of the Newtonian noise have heretofore been disregarded as they were considered negligible. However, we demonstrate that they are indeed not far from the realm of being measurable. They could be used to validate Einsteinian general relativity or to give valuable information on the true dynamical nature of gravity. One fundamental question, for example, is a direct measurement the speed of propagation of gravitational effects and the verification that it is indeed the same as the speed of light. We propose a simple laboratory experiment that could affirm or deny this proposition. We also analyze the possibility of the detection of large geophysical events, such as earthquakes. We find that large seismic events seem to be easily observable with the present ensemble of gravitational wave detectors,. The ensemble of gravitational wave detectors could easily serve as a system of early warning for otherwise catastrophic seismic events.
The Euclidean path integral quite often involves an action that is not completely real {it i.e.} a complex action. This occurs when the Minkowski action contains $t$-odd CP-violating terms. Analytic continuation to Euclidean time yields an imaginary
term in the Euclidean action. In the presence of imaginary terms in the Euclidean action, the usual method of perturbative quantization can fail. Here the action is expanded about its critical points, the quadratic part serving to define the Gaussian free theory and the higher order terms defining the perturbative interactions. For a complex action, the critical points are generically obtained at complex field configurations. Hence the contour of path integration does not pass through the critical points and the perturbative paradigm cannot be directly implemented. The contour of path integration has to be deformed to pass through the complex critical point using a generalized method of steepest descent, in order to do so. Typically, what is done is that only the real part of the Euclidean action is considered, and its critical points are used to define the perturbation theory. In this article we present a simple 0+1-dimensional example, of $N$ scalar fields interacting with a U(1) gauge field, in the presence of a Chern-Simons term, where alternatively, the path integral can be done exactly, the procedure of deformation of the contour of path integration can be done explicitly and the standard method of only taking into account the real part of the action can be followed. We show explicitly that the standard method does not give a correct perturbative expansion.
