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We consider a theory in which spacetime is an n-dimensional surface Vn embedded in an N-dimensional space VN. In order to enable also the Kaluza- Klein approach we admit n > 4. The dynamics is given by the minimal surface action in a curved embedding space. The latter is taken, in our specific model, as being a conformally flat space. In the quantization of the model we start from a generalization of the Howe-Tucker action which depends on the embedding variablesa(x) and the (intrinsic) induced metric gµ on Vn. If in the path integral we perform only the functional integration overa(x), we obtain the effective action which functionally depends on gµ and contains the Ricci scalar R and its higher orders R2 etc. But due to our special choice of the conformal factor in VN enterig our original 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 a point particle. Thus, starting from the basic fieldsa(x), we induce not only the kinetic term for gµ, but also the "matter" source term. email: MATEJ.PAVSIC@IJS.SI

The embedding model of induced gravity with bosonic sources