Studying Ghosts in Field Theory with the Fully Implicit Spacetime Finite Element Method

In physics field theory, the term ghost refers to a system with a degree of freedom that contains a negative kinetic energy term. These systems have been deemed dynamically unstable and will evolve without bounds. However, recent studies have shown that this is not always the case: some ghost-ridden systems are dynamically stable. This research seeks to further the understanding of how different systems can survive while living with ghosts. The numerical method executed here is the fully implicit space time finite element method. So far, data has been produced for cases with dimensions of 1 + 1 (one spatial and one temporal) and 2 +1. This is leading up to the 3 + 1 case which is of real interest due to its ability to represent physically realizable states of nature. By using the fully implicit space time finite element method, we would like to simulate a system to observe dynamically stable or unstable behavior of a simple ghost-ridden system.