ИСТИНА

We analyze the gravity-induced effects associated with a massless scalar field in a higher-dimensional spacetime being the tensor product of (d-n)-dimensional Minkowski space and n-dimensional spherically/cylindrically-symmetric space with a solid/planar angle deficit. These spacetimes are considered as simple models for a multidimensional global monopole (if n>2) or cosmic string (if n=2) with (d-n-1) flat extra dimensions. Thus, we refer to them as conical backgrounds. In terms of the angular deficit value, we derive the perturbative expression for the scalar Green's function and compute it to the leading order. With the use of this Green's function we compute the renormalized vacuum expectation value of the scalar field square and the renormalized vacuum averaged of the scalar-field's energy-momentum tensor for arbitrary d and n and for arbitrary coupling constant to the curvature. In particular, we revisit the computation of the vacuum polarization effects for a non-minimally coupled massless scalar field in the spacetime of a straight cosmic string. To deal with divergences, which appear in consideration of the both problems, we apply the dimensional-regularization technique, widely used in quantum field theory. Finally, we consider the vacuum polarization in the connection with the point source with a zero-range potential, with the explicit construction of self-adjoint extension. The comparison with the basic computation made above, is discussed.