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Progress in effective field theory approach to the binary inspiral problem

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Abstract

In this article I review the progress made in understanding the binary in spiral problem using Effective Field Theory technology.

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Notes

  1. This talk is only concerned with classical relativity.

  2. This term is perhaps too strong a statement, as geometry always plays a role. The word demi-geometric would probably be more appropriate.

  3. It would appear to me, that the amount of effort going into analytic calculation has been dwarfed by the numerical effort especially within the United States. This is just the perception of an outsider and is completely anecdotal.

  4. In the old days these two theories would be called “non-renormalizable” and “renormalizable” respectively.

  5. Through out this article we will be using units. \(c=\hbar =1\).

  6. This is the case in QCD when one tries of determine the dynamics of low energy Goldstone bosons (pions). In this case one has to fix the coefficients \(C^\prime _i\) by using data.

  7. It is not always true that one can expand the propagators, in which case the action becomes non-local. In the non-relativistic case (PN) this leads to an action which is non-local in space, while in the EMRI case it’s non-local in time as well.

  8. We use this term, much to the dismay of many a referee, even when dealing with classical theories.

  9. In the case of classical EFT this is typically not true. For instance in the PN expansion every log is accompanied by factors of \(v\). Thus while the logs may dominate the terms at some fixed order in \(v\), re-summation does not improve the accuracy of the prediction.

  10. In the language of asymptotic expansions these correspond to the near and far fields.

  11. These diagrams which be two particle irreducible to avoid double counting. That is, one should not be able to disconnect the diagram by cutting the two matter worldliness.

  12. I thank Gerhard Schaefer for conversations on this result.

  13. For an alternative approach see [44, 45].

  14. Indeed we can choose to completely absorb the effect of these local operators in the correlation functions of the \(Q's\).

  15. In linear response theory the relevant correlator is retarded. However, away from the poles the retarded and time ordered products are identical.

  16. The time ordered product and the retarded correlator differ only in their treatment of the poles.

  17. Naively this amplitude is zero, however, if an external momentum is complexified this is not longer true. This complexification is necessary for the BCFW construction of recursion relations for the n-point on-shell S matrix element.

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Acknowledgments

I would like to thank the organizers of GR20-Amaldi10 for the invitation to speak and for their gracious hospitality. I would also like to thank my collaborators on this subject, Walter Goldberger and Rafael Porto.

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  1. Department of Physics, Carnegie Mellon University, 15213 , Pittsburgh, PA, USA

    Ira Z. Rothstein

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  1. Ira Z. Rothstein
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Correspondence to Ira Z. Rothstein.

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This article belongs to the Topical Collection: The First Century of General Relativity: GR20/Amaldi10.

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Rothstein, I.Z. Progress in effective field theory approach to the binary inspiral problem. Gen Relativ Gravit 46, 1726 (2014). https://doi.org/10.1007/s10714-014-1726-y

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