Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism

Motivated by the fermionic Berry’s phase in momentum space, we study a local Abelian phase in momentum space coupled to electromagnetism, for complex scalars in the phase-space worldline formalism. The interaction of both Abelian fields is shown to give rise to a momentum gauge dependent emergent spacetime. As a concrete example, we further study classical solutions of the Berry-inspired gauge field that lead to an emergent Newtonian gravity with gravitational potential predicted by coupled Coulomb fields both in configuration and momentum spaces. Noncommutative aspects of the theory are also provided.