THE EMBEDDING MODEL OF INDUCED GRAVITY WITH BOSONIC SOURCES

We consider a theory in which spacetime is a 4-dimensional manifold V- 4 embedded in an N-dimensional space V-N. The dynamics is given by a f irst-order action which is a straightforward generalization of the wel l-known Nambu-Gotto string action. Instead of the latter action we the n consider an equivalent action, a generalization of the Howe-Tucker a ction, which is a functional of the (extrinsic) embedding variables et a(a)(x) and of the (intrinsic) induced metric g(mu nu)(x) on V-4. In t he quantized theory we can define an effective action by means of the Feynman path integral in which we functionally integrate over the embe dding variables. What remains is functionally dependent solely an the induced metric. Ii is well known that the effective action so obtained contains the Ricci scalar R and its higher orders. But due to our spe cial choice of a quantity, the so-called ''matter'' density omega(eta) in V-N entering the original first-order action, ii turns out that th e effective action contains also the source term. The latter is in gen eral that of a p-dimensional membrane (p-brane). In particular we cons ider the case of bosonic point particles. Finally we discuss and clari fy certain interpretational aspects of quantum mechanics from the view point of our embedding model.