2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/34962It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a noncommutative generalisation of the Hamilton-Jacobi equation. If a certain form for the metric in the noncommuting coordinate system is assumed, along with a correspondence rule for the commutation relations, it can be argued that this noncommutative Hamilton-Jacobi equation is equivalent to standard quantum mechanics.5 pagesGeneral Relativity and Quantum CosmologyHigh Energy Physics - TheoryQuantum Physicstext