Pulsating Vacuum States

A function in projective space is introduced for describing matter states. Spacetime
is explained by additions on elliptic curves and chaotic one-dimensional
quadratic maps. The introduced vacuum state is like a paired superfluid state
of a non-Hermitian Hamiltonian. Doubly-periodic stable orbits are investigated
in a quadratic surrounding of nontrivial zeros of the zeta function. The relevant
partition function indicates phase transitions and predicts various vacuum states
in dependence on processing. Partition function zeros quadratic in two complex
masses and two complex curvatures of spacetime are predicted phase transitions
which are statistically dominating instead of being exceptional.