TITLE:
Pulsating Vacuum States
AUTHORS:
Otto Ziep
KEYWORDS:
Complex Lagrangian, Quadratic Newtonian Root Finding, Minkowski Spacetime, Green’s Function Singularity, Bifurcation, Elliptic Curves, Pulsating Vacuum State, Phase Transition
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.12 No.3,
June
23,
2026
ABSTRACT: 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.