Interaction of Photons and Gravitons

The Hamiltonian formulation of general relativity is employed to study the interaction of photons and gravitons in the first approximation. The redundant variables are eliminated by an appropriate choice of gauge and coordinate conditions. $S$-matrix elements are calculated for initial states in which one photon is present and final states in which a photon and a graviton are present. Self-energy effects appear in first order but contribute nothing. Energy and momentum can be strictly conserved only if the initial and final photons and the gravitons all propagate in the same direction. For this case the $S$-matrix elements vanish in consequence of the null character of the Maxwell field, and the transition probability is also zero. Energy need not be exactly conserved if the process occurs at a rate which is sufficiently high. Under these conditions, corresponding to energies≫${10}^{28}$ eV, a photon might decay into another photon and a graviton. The graviton has very low energy. This cannot explain the red shift as a "tired light" phenomenon. The creation of gravitons by Coulomb scattering of photons and by scattering in a magnetostatic field is shown to occur and the cross sections are calculated.