The Reconstruction Principle A Common Mathematical Origin of Green Functions, Hilbert Spaces, and Spacetime
Borros Arneth
Modern theoretical physics employs several fundamental mathematical structures, including Green functions, Hilbert spaces, operator algebras, Gibbs ensembles, gauge fields, and spacetime geometry. These structures are traditionally introduced independently and serve as separate foundations for quantum mechanics, quantum field theory, statistical mechanics, and general relativity. In the present work, we propose an alternative mathematical organization based on a single Reconstruction Principle. Beginning with one primitive mathematical architecture, successive reconstruction layers generate transport operators, Green functions, Diagram Hilbert Spaces, complex quantum operators, Gibbs ensembles, entropic projections, and finally macroscopic spacetime together with gauge fields. Each layer is reconstructed uniquely from its predecessor without introducing additional primitive mathematical structures. Consequently, Hilbert space, Green functions, and spacetime are interpreted as successive mathematical representations of one underlying architecture rather than independent foundations. The resulting reconstruction hierarchy provides a unified conceptual framework connecting quantum mechanics, statistical mechanics, gauge theory, and emergent gravity while substantially reducing the number of independent assumptions.
•Jun 27, 2026•0 citations