The embedding model of induced gravity with bosonic sources

Foundations of Physics 24 (11):1495-1518 (1994)

We consider a theory in which spacetime is a 4-dimensional manifold V4 embedded in an N-dimensional space VN. The dynamics is given by a first-order action which is a straightforward generalization of the well-known Nambu-Gotto string action. Instead of the latter action we then consider an equivalent action, a generalization of the Howe-Tucker action, which is a functional of the (extrinsic) embedding variables ηa(x) and of the (intrinsic) induced metric gυv (x) on V4. In the quantized theory we can define an effective action by means of the Feynman path integral in which we functionally integrate over the embedding variables. What remains is functionally dependent solely on the induced metric. It is well known that the effective action so obtained contains the Ricci scalar R and its higher orders. But due to our special choice of a quantity, the so-called “matter” density ω(η) in VN entering the original first-order action, it turns out that the effective action contains also the source term. The latter is in general that of a p-dimensional membrane (p-brane). In particular we consider the case of bosonic point particles. Finally we discuss and clarify certain interpretational aspects of quantum mechanics from the viewpoint of our embedding model
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DOI 10.1007/BF02054780
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