Worldline approach to eikonals for QED and linearized quantum gravity and their off mass shell extensions

Physics

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Specific Calculations, Quantum Gravity, Approximations

Scientific paper

We construct the worldline expression pertaining to a four-point process involving the scattering of two spin-1/2 particles via photon exchange. Restricting our attention to the case of forward scattering at extremely high energies, we show how to formulate the corresponding eikonal version of the four-point Green's function. We proceed to distinguish between the on and off mass shell cases within the framework of our description. For the on mass shell situation we recover the well-known result for the QED eikonal which corresponds to the infinite Coulomb phase. The (slightly) off mass shell case is confronted next. We produce a relevant expression for the eikonal phase in analytic form. Finally, we extend our considerations to a linearized quantum gravitational model and recover, via a series of elementary steps, the 0th order eikonal result for Planckian scattering (both for on and off mass shell).

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