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We evaluate the four-closed-string scattering amplitude, using the Polyakovstring path integral in the proper-time gauge. By identifying the Fock spacerepresentation of the four-closed-string-vertex, we obtain a field theoreticexpression of the closed string scattering amplitudes. In the zero-slope limit,the four-closed-string scattering amplitude reduces to thefour-graviton-scattering amplitude of Einstein's gravity. However, at a finiteslope, the four-graviton scattering amplitude in the proper-time gauge differsnot only from that of Einstein gravity, but also significantly differs from theconventional one obtained by using the vertex operator technique in stringtheory. This discrepancy is mainly due to the presence of closed string tachyonpoles in the four-graviton-scattering amplitude, which are missing in previousworks. Because the tachyon poles in the scattering amplitude considerably alterthe short distance behavior of gravitational interaction, they may be importantin understanding problems associated with the perturbative theory of quantumgravity and the dark matter within the framework of string theory.

Four-Graviton Scattering and String Path Integral in the Proper-time gauge