Investigation of the High Energy Behaviours of the Scalar Particle Scattering Amplitude in the Gravitational Field by Functional Approach†

Closed expressions for the Green function and amplitude of the scalar particle scattering in the external gravitational field gμν(x) are found in the form of functional integrals. It is shown that, as compared with the scattering on the vector potential, the tensor character of the gravitational field leads to a more rapid increase of the cross section with increasing energy. Discrete energy levels of particles are obtained in the Newton potential. PACS Numbers : 11.10 field theory, 12.20 fundamental interactions November 1994 CPT-94/P.3084 anonymous ftp or gopher: cpt.univ-mrs.fr Unité Propre de Recherche 7061 To submitted to Nuovo Cimento A. Permanent address: Department of Theoretical Physics, Hanoi State University, P. O. Box 600, BoHo, Hanoi, 10000, Vietnam