Natural discrete differential calculus in physics

Carlo Rovelli (1) , Václav Zatloukal (1)

1 CPT - Centre de Physique Théorique - UMR 7332

We sharpen a recent observation by Tim Maudlin: differential calculus is a natural language for physics only if additional structure, like the definition of a Hodge dual or a metric, is given, but the discrete version of this calculus provides this additional structure for free.

Mots clés: differential forms; simplex; field theory: discrete; lattice field theory; mathematical methods; Field theory; Quantum gravity; Structure of space; duality; differential geometry

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Réseau [hep-lat]

Carlo Rovelli, Václav Zatloukal. Natural discrete differential calculus in physics. 2024. ⟨hal-02051474⟩