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Illuminating Light Bending

N. E. J. Bjerrum-Bohr, Barry R. Holstein, John F. Donoghue, Ludovic Planté, Pierre Vanhove

TL;DR

The paper extends the 'gravity is the square of a gauge theory' framework to spin-1 targets, showing graviton amplitudes factorize into a universal kinematic factor times electromagnetic amplitudes and revealing spin-independent universality in various limits. By deriving graviton photo-production and gravitational Compton scattering for a spin-1 target, and analyzing the massless limit, it demonstrates that graviton interactions can be computed from elementary EM processes, and it clarifies the correct photon–graviton cross-section by handling the longitudinal degrees of freedom. The work then connects quantum scattering to classical light bending via three complementary routes—quantum amplitude, geometrical optics, and the eikonal approach—showing consistent results for the leading and next-to-leading bending angles θ=4GM/b and θ_1=15π G^2M^2/(4b^2). It also discusses graviton–graviton scattering via factorization and highlights forward-scattering peculiarities, including a γ-pole–driven divergence in graviton photo-production. Collectively, the results provide a pedagogical framework for incorporating quantum gravity processes into quantum mechanics courses and illuminate deep connections between gravity and gauge theories with potential astrophysical implications.

Abstract

The interactions of gravitons with spin-1 matter are calculated in parallel with the well known photon case. It is shown that graviton scattering amplitudes can be factorized into a product of familiar electromagnetic forms, and cross sections for various reactions are straightforwardly evaluated using helicity methods. Universality relations are identified. Extrapolation to zero mass yields scattering amplitudes for photon-graviton and graviton-graviton scattering. The phenomenon of light bending near a massive object, which is generally treated using classical general relativity, is discussed from alternative points of view.

Illuminating Light Bending

TL;DR

The paper extends the 'gravity is the square of a gauge theory' framework to spin-1 targets, showing graviton amplitudes factorize into a universal kinematic factor times electromagnetic amplitudes and revealing spin-independent universality in various limits. By deriving graviton photo-production and gravitational Compton scattering for a spin-1 target, and analyzing the massless limit, it demonstrates that graviton interactions can be computed from elementary EM processes, and it clarifies the correct photon–graviton cross-section by handling the longitudinal degrees of freedom. The work then connects quantum scattering to classical light bending via three complementary routes—quantum amplitude, geometrical optics, and the eikonal approach—showing consistent results for the leading and next-to-leading bending angles θ=4GM/b and θ_1=15π G^2M^2/(4b^2). It also discusses graviton–graviton scattering via factorization and highlights forward-scattering peculiarities, including a γ-pole–driven divergence in graviton photo-production. Collectively, the results provide a pedagogical framework for incorporating quantum gravity processes into quantum mechanics courses and illuminate deep connections between gravity and gauge theories with potential astrophysical implications.

Abstract

The interactions of gravitons with spin-1 matter are calculated in parallel with the well known photon case. It is shown that graviton scattering amplitudes can be factorized into a product of familiar electromagnetic forms, and cross sections for various reactions are straightforwardly evaluated using helicity methods. Universality relations are identified. Extrapolation to zero mass yields scattering amplitudes for photon-graviton and graviton-graviton scattering. The phenomenon of light bending near a massive object, which is generally treated using classical general relativity, is discussed from alternative points of view.

Paper Structure

This paper contains 18 sections, 167 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Spin One Interactions: a Lightning Review
  3. Compton Scattering
  4. Gravitational Interactions
  5. Graviton Photo-production
  6. Gravitational Compton Scattering
  7. Graviton-Photon Scattering
  8. Extra Credit
  9. The forward cross-section
  10. Bending of Light in Classical General Relativity
  11. Quantum Mechanical Scattering Amplitude
  12. Geometrical Optics
  13. Small-Angle Scattering (Eikonal) Method
  14. Conclusion
  15. Equivalence between eikonal and geometrical optics
  16. ...and 3 more sections

Figures (5)

  • Figure 1: Diagrams relevant to Compton scattering.
  • Figure 2: (a) The one-graviton and (b) two-graviton emission vertices from either a scalar, spinor or vector particle.
  • Figure 3: The three graviton vertex
  • Figure 4: Diagrams relevant to graviton photo-production.
  • Figure 5: Diagrams relevant for gravitational Compton scattering.