Feynman graph derivation of the Einstein quadrupole formula

Abstract

The one-graviton transition operator and, consequently, the classical energy-loss formula for gravitational radiation are derived from the Feynman graphs of helicity+or-2 theories of gravitation. The calculations are done both for the case of electromagnetic and gravitational scattering. The departure of the in and out states from plane waves owing to the long-range nature of gravitation is taken into account to improve the Born approximation calculations. This also includes a long-range modification of the graviton wavefunction which is shown to be equivalent to the classical problem of the true light cones deviating logarithmically at large distances from the flat space light cones. The transition from the S-matrix elements calculated graphically to the graviton transition operator is done by using complementarity of space-time and momentum descriptions. The energy-loss formula drove originally by Einstein is shown to be correct.