Gravitational Quadratic-in-Spin Hamiltonian at NNNLO in the post-Newtonian framework

Abstract

We present the result of the quadratic-in-spin interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to N 3 LO corrections within the post-Newtonian expansion. The calculation is performed by employing the effective field theory diagrammatic approach, and it involves Feynman integrals up to three loops, evaluated within the dimensional regularization scheme. The gauge-invariant binding energy and the scattering angle, in special kinematic regimes and spin configurations, are explicitly derived. The results extend our earlier study on the spin-orbit interaction effects.

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

“…The observations of gravitational waves from compact binary coalescence [4,5] have necessitated a better understanding of compact binary dynamics, attracting practitioners of quantum field theory (QFT) to develop QFT-inspired methods for handling the relativistic two-body problem . An important aspect of relativistic two-body dynamics is the effects of spin, where QFT-inspired methods have proved to be powerful tools for their understanding, as can be inferred from the vast number of recent works on the subject; post-Newtonian effective field theory (PNEFT) [49][50][51][52][53][54][55][56][57][58][59], scattering amplitudes [1,2,[60][61][62][63][64][65][66][67][68][69][70][71][72], post-Minkowskian effective field theory [73], and worldline quantum field theory (WQFT) [74][75][76][77][78]. Of course, each approach comes with its own shortcomings; e.g.…”