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Classical BMS\(_3\) Symmetry

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BMS Particles in Three Dimensions

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Abstract

The Bondi–Metzner–Sachs (BMS) group is an infinite-dimensional symmetry group of asymptotically flat gravity at null infinity, that extends Poincaré symmetry.

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Notes

  1. 1.

    We are cheating in (9.8), since for now there is no way to distinguish \(X'''(\varphi )\) from \(-X'(\varphi )\); the justification for this combination of derivatives will be provided by asymptotic symmetries.

  2. 2.

    The prefix “super” has nothing to do with supersymmetry, but stresses the fact that special-relativistic quantities are extended in an infinite-dimensional way.

  3. 3.

    Indeed, changing the normalization of p would also change the value of the central charge that ensures that the bracket \(\{{\mathcal J},{\mathcal P}\}\) takes the canonical form in Eq. (9.37).

  4. 4.

    In case of identical notations, the subscript indicates which group we are referring to.

  5. 5.

    As in Chap. 6 we describe diffeomorphisms of the circle by their lifts belonging to the universal cover \(\widetilde{\text {Diff}}{}^+(S^1)\), which we abusively denote simply as \(\text {Diff}(S^1)\).

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  1. Institute for Theoretical Physics, ETH Zürich, Zürich, Switzerland

    Blagoje Oblak

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Oblak, B. (2017). Classical BMS\(_3\) Symmetry. In: BMS Particles in Three Dimensions. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-61878-4_9

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