Abstract
We apply the classical double copy to the calculation of self-energy of composite systems with multipolar coupling to gravitational field, obtaining next-to-leading order results in the gravitational coupling GN by generalizing color to kinematics replacement rules known in literature. When applied to the multipolar description of the two-body system, the self-energy diagrams studied in this work correspond to tail processes, whose physical interpretation is of radiation being emitted by the non-relativistic source, scattered by the curvature generated by the binary system and then re-absorbed by the same source. These processes contribute to the conservative two-body dynamics and the present work represents a decisive step towards the systematic use of double copy within the multipolar post-Minkowskian expansion.
Highlights
For other relevant work on the classical double copy: see [14] for application to the twobody effective gravitational potential in the post-Newtonian approximation, with possible problems arising at O(G2N ) with respect to leading order [15], and the seminal work [16, 17] for the determination of the two-body potential at third post-Minkowskian order
When applied to the multipolar description of the two-body system, the self-energy diagrams studied in this work correspond to tail processes, whose physical interpretation is of radiation being emitted by the non-relativistic source, scattered by the curvature generated by the binary system and re-absorbed by the same source
In the present work we show the computation of self-energy diagrams representing forward scattering of non-relativistic sources described by their multipolar coupling to gauge and gravity fields to next-to-leading order in the gauge/gravity coupling, by extending previously derived rules for gauge charge/kinematic variable duality
Summary
We show how the mapping between the square of gauge amplitudes and gravity ones work in the case of multipole-expanded sources. On the gauge side we consider the bulk action. Vectors), and a system of classical, spinning Yang-Mills color charges coupled to gluons, described by a trajectory xμ, a color charge ca and a spin Sμν (all three depending on the world-line parameter τ ), whose dynamics is described by the world-line action summed over particles. The spin antisymmetric tensor Sμν has 6 components, we adopt a spin supplementary condition [22]. On the gravity side we have that the degrees of freedom are represented by the metric gμν, the dilaton ψ and the axion Bμν with field strength Hμνρ defined by.
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