Dressing the Post-Newtonian two-body problem and Classical Effective Field Theory

Abstract

We apply a dressed perturbation theory to better organize and economize the computation of high orders of the 2-body effective action of an inspiralling Post-Newtonian gravitating binary. We use the effective field theory approach with the non-relativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a non-linear classical field theory coupled to point-like sources. We introduce dressed charges and propagators, but unlike the quantum theory there are no dressed bulk vertices. The dressed quantities are found to obey recursive integral equations which succinctly encode parts of the diagrammatic expansion, and are the classical version of the Schwinger-Dyson equations. Actually, the classical equations are somewhat stronger since they involve only finitely many quantities, unlike the quantum theory. Classical diagrams are shown to factorize exactly when they contain non-linear world-line vertices, and we classify all the possible topologies of irreducible diagrams for low loop numbers. We apply the dressing program to our Post-Newtonian case of interest. The dressed charges consist of the dressed energy-momentum tensor after a non-relativistic decomposition, and we compute all dressed charges (in the harmonic gauge) appearing up to 2PN in the 2-body effective action (and more). We determine the irreducible skeleton diagrams up to 3PN and we employ the dressed charges to compute several terms beyond 2PN.

38 pages, 28 figures. PRD published version, added references

References in corpus (20)

• Relativistic tidal properties of neutron stars
• Relativistic theory of tidal Love numbers
• Essentials of Blackfold Dynamics
• Hamiltonian of a spinning test-particle in curved spacetime
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Effective field theory calculation of second post-Newtonian binary dynamics
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• Non-Relativistic Gravitation: From Newton to Einstein and Back
• Classical Effective Field Theory and Caged Black Holes
• On the gravitational polarizability of black holes
• Towards an S-matrix Description of Gravitational Collapse
• Les Houches Lectures on Effective Field Theories and Gravitational Radiation
• The n-body problem in General Relativity up to the second post-Newtonian order from perturbative field theory
• Asymptotics of d-dimensional Kaluza-Klein black holes: beyond the Newtonian approximation
• Canonical formulation of self-gravitating spinning-object systems
• Gravitational radiation in d>4 from effective field theory
• Caged black hole thermodynamics: Charge, the extremal limit, and finite size effects
• The Delocalized Effective Degrees of Freedom of a Black Hole at Low Frequencies
• Post-Newtonian theory and the two-body problem
• Post-Newtonian methods: Analytic results on the binary problem

Cited by in corpus (21)

• Amplitudes, Observables, and Classical Scattering
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Gravitational radiative corrections from effective field theory
• Effective field theory calculation of conservative binary dynamics at third post-Newtonian order
• Effective field theory methods to model compact binaries
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Multipole expansion at the level of the action
• Canonical Formulation of Spin in General Relativity
• Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians
• Next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for self-gravitating binaries
• Point-Particle Effective Field Theory I: Classical Renormalization and the Inverse-Square Potential
• Einstein's action and the harmonic gauge in terms of Newtonian fields
• Elimination of the spin supplementary condition in the effective field theory approach to the post-Newtonian approximation
• Theory of post-Newtonian radiation and reaction
• A nonlinear scalar model of extreme mass ratio inspirals in effective field theory II. Scalar perturbations and a master source
• Classical 3-loop 2-body diagrams
• Parametrized Tidal Dissipation Numbers of Non-rotating Black Holes
• Dynamical Tidal Response of Non-rotating Black Holes: Connecting the MST Formalism and Worldline EFT
• Classical Effective Field Theory for Weak Ultra Relativistic Scattering
• Love beyond Einstein: Metric reconstruction and Love number in quadratic gravity using WEFT