TY - JOUR

T1 - Dressing the post-Newtonian two-body problem and classical effective field theory

AU - Kol, Barak

AU - Smolkin, Michael

PY - 2009/12/29

Y1 - 2009/12/29

N2 - 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 (PN) gravitating binary. We use the effective field theory approach with the nonrelativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a nonlinear classical field theory coupled to pointlike 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 nonlinear worldline 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 nonrelativistic 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.

AB - 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 (PN) gravitating binary. We use the effective field theory approach with the nonrelativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a nonlinear classical field theory coupled to pointlike 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 nonlinear worldline 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 nonrelativistic 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.

UR - http://www.scopus.com/inward/record.url?scp=73449134772&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.80.124044

DO - 10.1103/PhysRevD.80.124044

M3 - Article

AN - SCOPUS:73449134772

SN - 1550-7998

VL - 80

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 12

M1 - 124044

ER -