High-energy scattering of a scalar particle in a gravitational field

Expressions for Green's function and amplitude of scattering of a scalar particle in an external gravitational field g_{μν}(х) in closed form in the form of functional integrals are found. It is shown that the tensor nature of the gravitational field results in a more rapid growth of a cross section with energy, as compared with the scattering on a vector potential. Discrete energy levels of a particle in a Newtonian potential are obtained.