Non-minimal Coupling from Consistency Requirements for a Localization Operator
arXiv:2004.00826
Abstract
Requiring both that a proposed localization-density operator be linear in quantum theory and that its expectation value be covariant leads to addition of terms in the Hamiltonian, coupling a scalar field to a connection on the vector-density bundle. This would appear to implicate spacetime geometry in the scalar's dynamics to a greater degree than what is prescribed by minimal coupling.
Essay written for the Gravity Research Foundation 2020 Awards for Essays on Gravitation. (5 pages)