### abstract

- We study models where the gauge coupling constants, masses and the gravitational constant are functions of some conserved charge in the universe, and furthermore a cosmological constant that depends on the total charge of the universe. We first consider the standard Dirac action, but where the mass and the electromagnetic coupling constant are a function of the charge in the universe and afterwards extend this to curved spacetime and consider gauge coupling constants, the gravitational constant and the mass as a function of the charge of the universe, which represent a sort of Mach principle for all the constants of nature. In the flat space formulation, the formalism is not manifestly Lorentz invariant, however Lorentz invariance can be restored by performing a phase transformation of the Dirac field. One interesting model of this type is one where the action is invariant under rescalings of the Dirac wave function. In the curved space time formulation, there is the additional feature that some of the equations of motion break the general coordinate invariance also, but in a way that can be understood as a coordinate choice only, so the equations are still of the General Relativity type, but with a certain natural coordinate choice, where there is no current of the charge. We have generalized what we have done and also constructed a cosmological constant which depends on the total charge of the universe. We discuss how these ideas work when the space where the charges live is finite. If we were to use some only approximately conserved charge for these constructions, like say baryon number (in the context of the standard model), this will lead to corresponding violations of Lorentz symmetry in the early universe for example. We also briefly discuss another non-local formulations where the coupling constants are functions of the Pontryagin index of some non-abelian gauge field configurations. The construction of charge dependent contributions can also be motivated from the structure of the “infra-red counter terms” needed to cancel infra red divergences for example in three dimensions.