On the Quantum Field Theory of the Interaction between the Graviton and the Matter Field
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In order to quantize the gravitational field so as to be consistent with the general relativistic treatment, we investigate what physical effects the quantizable and unquantizable parts of gravitational field have, when the matter fields exist. To construct the Hamiltonian, we show that the interaction Hamiltonian in the interaction representation can be obtained by the method extended from that of Yang-Feldman. The role of the non-linear part of gravitational field for such a problem is also discussed. Only the potential, obtained by eliminating the longitudinal and scalar parts of gravitational field with the aid of the supplementary condition, has an effect upon the macroscopical phenomena and gives the equation of two-body problem in general relativity found by Einstein, Infeld and Hoffmann. On the other hand, while the pure transverse graviton does not contribute to the macroscopical phenomena, it gives, in the region of high energy, the large damping effect upon the interaction between the elementary particles.
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