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.

arXiv comment33 pages; v2: references added, minor changes, version to be published

References in corpus (68)

• General relativity as an effective field theory: The leading quantum corrections
• An Effective Field Theory of Gravity for Extended Objects
• Perturbative Quantum Field Theory in the String-Inspired Formalism
• Amplitudes, Observables, and Classical Scattering
• Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses
• General Relativity from Scattering Amplitudes
• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• Classical black hole scattering from a worldline quantum field theory
• Observables and amplitudes for spinning particles and black holes
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• On-shell Techniques and Universal Results in Quantum Gravity
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Gravitational radiative corrections from effective field theory
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• Gravitomagnetic bending angle of light with finite-distance corrections in stationary axisymmetric spacetimes
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Factorization Properties of Soft Graviton Amplitudes
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• Bending of Light in Quantum Gravity
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• SUSY in the Sky with Gravitons
• Light-like Scattering in Quantum Gravity
• Universality in the classical limit of massless gravitational scattering
• On an Exponential Representation of the Gravitational S-Matrix
• Second-order Post-Minkowskian scattering in arbitrary dimensions
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• Worldline formalism in a gravitational background
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Trace Anomalies from Quantum Mechanics
• Gravitational spin Hall effect of light
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Worldline approach to vector and antisymmetric tensor fields
• Next-to-soft corrections to high energy scattering in QCD and gravity
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level
• Shadow and deflection angle of rotating black hole in asymptotically safe gravity
• Towers of Gravitational Theories
• Graviton-Photon Scattering
• Wilson line approach to gravity in the high energy limit
• Classical observables from coherent-spin amplitudes
• Planckian Energy Scattering and Surface Terms in the Gravitational Action
• Classical Yang-Mills observables from amplitudes
• Classical Double Copy of Worldline Quantum Field Theory
• Worldline approach to vector and antisymmetric tensor fields II
• Infrared Divergences and the Eikonal Exponentiation
• Propagation of polarized gravitational waves
• Particles with non abelian charges
• More on the Bending of Light in Quantum Gravity
• One-particle reducible contribution to the one-loop spinor propagator in a constant field
• Asymptotic dynamics on the worldline for spinning particles
• Multiphoton amplitudes and generalized LKF transformation in Scalar QED
• Bern-Kosower Rule for Scalar QED
• Dressed scalar propagator in a non-abelian background from the worldline formalism
• Worldline master formulas for the dressed electron propagator, part 1: Off-shell amplitudes
• One-particle reducible contribution to the one-loop scalar propagator in a constant field
• Extended SUSY quantum mechanics: transition amplitudes and path integrals
• Worldline master formulas for the dressed electron propagator, part 2: On-shell amplitudes
• Classical and quantum gravitational scattering with Generalized Wilson Lines
• Quantum theories of (p,q)-forms
• Quantum theory of massless (p,0)-forms
• Worldline description of a bi-adjoint scalar and the zeroth copy
• The Equivalence Principle in a Quantum World
• Dressed Dirac Propagator from a Locally Supersymmetric $\mathcal{N}=1$ Spinning Particle
• A path integral description of quantum nonlinear optics in arbitrary media
• Classical gravitational scattering from a gauge-invariant double copy
• One-loop quantum gravity from a worldline viewpoint

Cited by in corpus (12)

• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Classical vs Quantum Eikonal Scattering and its Causal Structure
• Spinning waveforms from KMOC at leading order
• Boundary to bound dictionary for generic Kerr orbits
• Observables from classical black hole scattering in Scalar-Tensor theory of gravity from worldline quantum field theory
• Classical off-shell currents
• Binary Dynamics from Worldline QFT for Scalar-QED
• Spin supplementary condition in quantum field theory: covariant SSC and physical state projection
• Wave scattering event shapes at high energies
• Charged test-particle scattering and effective one-body metrics with spin
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT