Covariant Information Field Theory
Jim Harlow, Phil Tetlow, Oleg Salakhov
We present a structural framework for analyzing dynamics in background-independent theories based on admissible transport on configuration spaces. The approach reformulates canonical evolution not in terms of a fixed Hamiltonian, but via constrained transport maps acting on an admissible subspace of states, preserving constraint closure and covariance by construction. Within this setting, we show that admissible dynamics admit a dual description in terms of state transport and observable transport, related by an adjoint pairing, and we establish conditions under which validation metrics are invariant under this duality. We further prove that admissibility enforces contraction bounds on accumulated deviations under composition, providing a structural explanation for stability without specifying a particular microscopic dynamics. The framework is applied to canonical Loop Quantum Gravity as a consistency analysis rather than as a proposal for new dynamics. We clarify how transport-based formulations relate to existing spin- network and spin-foam constructions, and we identify precise conditions under which such formulations remain anomaly-free. No claim is made to resolve the full dynamics problem or to derive novel physical predictions. Instead, the results provide a controlled language for distinguishing structurally stable evolutions from inadmissible ones in background-independent quantum theories. This work is an information-theoretic framework concerned with admissible transport and stability of information under composition. Physical theories, including Loop Quantum Gravity (LQG), are used solely as structured test cases rather than as the primary object of study. LQG serves as a representative background-independent information system. This manuscript is information theory under constraints, not physics. CIFT is an information-theoretic framework in which conserved quantities are measured in bits and are conditional on explicit admission and boundary exchange.
•Mar 27, 2015•0 citations