How to change the sign of energy? - Report on my three months visit to YITP

Abstract

In this report I review some of my research activities during my visit to the Yukawa Institute for Theoretical Physics in Kyoto. In particular, during these three months, I was interested in explicitly time-dependent canonical transformations. These transformations map Hamiltonian equations into other Hamiltonian equations and are especially interesting in the context of cosmology. Indeed, there the focus is on the perturbations around time-dependent cosmological backgrounds, so that the Hamiltonian for perturbations is explicitly timedependent. Especially, the time-dependent canonical transformations are helpful for a reformulation of theories with ghosts–cosmological perturbations with the negative kinetic energies. During my stay at YITP, I have proven that one can always perform such a canonical transformation that a new description of the system does not involve ghost degrees of freedom.