Light bending from eikonal in worldline quantum field theory

Abstract

Using the worldline quantum field theory (WQFT) formalism for classical scattering, we study the deflection of light by a heavy massive spinless/spinning object. WQFT requires the use of the worldline dressed propagator of a photon in a gravitational background, which we construct from first principles. The action required to set up the worldline path integral is constructed using auxiliary variables, which describe dynamically the spin degrees of freedom of the photon and take care of path ordering. We test the fully regulated path integral by recovering the photon-photon-graviton vertex. With the dressed propagator at hand, we follow the WQFT procedure by setting up the partition function and deriving the Feynman rules which can be used to evaluate it perturbatively. These rules depend on the auxiliary variables. The latter ultimately do not contribute in the geometric-optics regime, which realizes the equivalence between the scattering of a photon and a massive scalar with that of a massless and a massive scalar. Then, the calculation of the eikonal phase and the deflection angle simplifies considerably. Using the eikonal phase defined in terms of the partition function, we calculate explicitly the deflection angle at NLO in the spinless case, and at LO in the spinning case up to quadratic order in spin.

Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory

“…The use of an N = 2 supersymmetric extension to the point-particle action to encapsulate spin degrees of freedom [116,117] circumvents the need for a local co-rotating frame. Recent work on the WQFT has included the double copy [118] and applications to light bending [119]; other closely related approaches involve directly solving the classical equations of motion [120] and Wilson line operators [121].…”

Spin supplementary condition in quantum field theory, Part I : covariant SSC and physical state projection

“…(2.8) by attempting to write it as a worldline action, following a procedure similar to that of ref. [104]. Up to total derivatives, the vector QED action for H = 0 can be written as…”

Binary Dynamics from Worldline QFT for Scalar-QED

“…WQFT is expected to have the potential of capturing such generating functions too. The classical eikonal phase can be obtained from WQFT in various contexts up to 2PM/next-to-leading order (NLO) [43,49,59,60]. However, the calculation of the eikonal phase at 3PM and beyond in WQFT remains somewhat ambiguous in the iǫ-prescription of the worldline propagator, due to the lack of a "natural" time order, as opposed to in the cases of the momentum impulse and spin kick.…”