Dynamical Informational Field Theory (DIFT): A Geometric Sigma–Model with Dynamostasis

Description This record presents the first complete formulation of Dynamical Informational Field Theory (DIFT). In DIFT, the fundamental field is a map from spacetime into an informational manifold equipped with a Fisher or quantum-Fisher type metric. The spacetime metric is fully dynamical (Einstein-Hilbert term), while the map field evolves as a curved-target sigma-model. A key feature of the theory is “dynamostasis”: a scalar constructed from the pullback of the informational metric is constrained to remain on a prescribed plateau. This produces a coupled Einstein–sigma-model system with a non-trivial constraint force. The manuscript derives the full field equations, the corresponding stress-energy tensor, and the resulting Einstein equations. As a concrete example, the paper develops a 4-dimensional informational manifold based on the quantum-Fisher geometry of pure two-mode Gaussian states (two-mode squeezed light). The coordinates are the local squeezing parameters and a relative phase, and the metric is given explicitly. This provides a practical and computable target space for DIFT, enabling the modelling of spacetime-dependent informational profiles inspired by continuous-variable entanglement, while keeping the entire framework strictly classical and geometric.