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Quantum BMS\(_3\) Symmetry

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BMS Particles in Three Dimensions

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

This chapter is devoted to irreducible unitary representations of the BMS\(_3\) group, i.e. BMS\(_3\) particles, which we classify and interpret. As we shall see, the classification is provided by supermomentum orbits that coincide with coadjoint orbits of the Virasoro group.

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Notes

  1. 1.

    We recall that the definition of quasi-invariant measures was given in Sect. 3.2.

  2. 2.

    Note that the existence of a quasi-invariant measure \(d\mu (q)\) on \({\mathcal O}_p\) implies the existence of infinitely many other ones, since one can always multiply the measure by a strictly positive smooth function \(\rho (q)\) and obtain a new measure \(\rho (q)d\mu (q)\).

  3. 3.

    To our knowledge there is, at present, no detailed review on BMS symmetry. Accordingly the literature review provided here cannot fail to be biased by the author’s ignorance; we apologize in advance for the references that we may have missed.

  4. 4.

    Recall that we use the same notation for both the \(\mathfrak {bms}_3\) algebra and its central extension.

  5. 5.

    I am indebted to Axel Kleinschmidt for this observation.

  6. 6.

    This occurrence of the \(\mathfrak {bms}_3\) algebra predates its gravitational description [127] by a decade!

  7. 7.

    Here \(\delta \) denotes the delta function associated by (3.39) with the measure \(\mu \).

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    Blagoje Oblak

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Oblak, B. (2017). Quantum BMS\(_3\) Symmetry. In: BMS Particles in Three Dimensions. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-61878-4_10

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