Inevitability of the Poisson Bracket Structure of the Relativistic Constraints

Abstract The purpose of this paper is to shed some fresh light on the long-standing conceptual question origin well-known Poisson bracket structure constraints that govern canonical dynamics generally relativistic field theories, i.e. geometrodynamics. This has long been known be same for a wide class fields inhabit space-time, namely those with non-differential coupling gravity. It also noticed an identical can derived independently any dynamical theory, by purely geometrical considerations in Lorentzian geometry. Here we attempt provide missing link between and geometry, which understand reason specific kind. We achieve careful analysis geometrodynamical approach, allows us derive it as consistency requirement such theory. In order stay close classical literature subject stick metric formulation general relativity, but reasoning should carry over other non-metricity tensor vanishes. discussion section devoted interesting consequences presented result context reconstructing Arnowitt–Deser–Misner (ADM) framework, thus providing precise sense inevitability Einstein’s theory under minimal assumptions.