  The quantization of higher order time derivative theories including
interactions is unclear. In this paper in order to solve this problem, we
propose to consider a complex version of the higher order derivative theory and
map this theory to a real first order theory. To achieve this relationship, the
higher order derivative formulation must be complex since there is not a real
canonical transformation from this theory to a real first order theory with
stable interactions. In this manner, we work with a non-Hermitian higher order
time derivative theory. To quantize this complex theory, we introduce reality
conditions that allow us to map the complex higher order theory to a real one,
and we show that the resulting theory is regularizable and renormalizable for a
class of interactions.

High Energy Physics - Theory