Exploring Stable Dynamics of Field Theory with Ghosts Using the Spacetime Finite Element Method

Systems that contain ghosts have always been considered unstable because they reach a singularity or "blow up" after a finite time. They contain a negative kinetic energy term and time derivatives higher than second order; this is why the Ostragradsky ghost originates. However, recent studies have shown that stable ghost systems can exist. The goal of this research is to investigate these phenomena: models in 1+1 (1 spatial and 1 temporal) and 2+1-dimensional cases were created to observe how a ghost system evolves. This was done by implementing our code using C and PETSc (The Portable, Extensible Toolkit for Scientific Computation). The numerical approach is based on the fully implicit spacetime finite element method, which numerically solves our wave-like ghost system with periodic boundary conditions. Future work will involve creating a large-scale 3+1 model to observe how the system evolves. Once successful, we can extend this to treating the system with more generally curved space time.