2021/12/31 by Fiorenzo Bastianelli, Francesco Comberiati, Leonardo de la Cruz · 34 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Eikonal equation #Feynman diagram #Gravitation #Graviton #Massless particle #Path integral formulation #Photon #Physics #Propagator #Pulsars and Gravitational Waves Research #Quantum #Quantum electrodynamics #Quantum field theory #Quantum mechanics #gr-qc #hep-th
paper · pdf · open access · doi:10.1007/jhep02(2022)209
published in Journal of High Energy Physics 2022(2) (Springer Nature) · 33 pages; v2: references added, minor changes, version to be published
openalex publication_date 2022/02/01 · arxiv created 2022/03/01 · arxiv updated 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.