Abstract
We consider the ADM splitting of the Einstein–Hilbert action in five dimensions in the presence of matter that can be either a “point particle”, or a set of scalar fields. The Hamiltonian, being a linear superposition of constraints, is equal to zero. Upon quantization, we obtain the Schrödinger equation for a wave functional, Ψ, that depends on the matter degrees of freedom, and on the 5D gravity degrees of freedom. After the Kaluza–Klein splitting, the functional Schrödinger equation decomposes so that it contains a part due to 4D gravity, a part due to electrodynamics, and a part due to matter. Depending on choice of the matter term, we obtain two different versions of a modified quantum electrodynamics. In one version, time automatically appears, and there is no problem with infinite vacuum energy density of matter fields, whereas in the other version such problems exist.
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