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Partition Functions and Characters

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BMS Particles in Three Dimensions

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

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Abstract

The asymptotic symmetries described in Chap. 9 suggest that the quantization of asymptotically flat gravitational fields in three dimensions provides unitary representations of BMS\(_3\).

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Notes

  1. 1.

    More precisely, the field at time \(\tau +\beta \) is rotated by \(\vec \theta \) with respect to the field at time \(\tau \).

  2. 2.

    Note also that the scalar heat kernel coincides with the propagator of a free particle in \(\mathbb {R}^D\), whose expression for \(D=2\) was written in Eq. (5.158).

  3. 3.

    An interesting problem is to understand if these algebras are merely different because of an unfortunate choice of basis, or if they are genuinely distinct in the sense that they are not isomorphic. We will not address this issue here.

  4. 4.

    Eventually these numbers will be exponentials of angular potentials, so they are fugacities associated with the rotation generators \(H_i\).

  5. 5.

    See e.g. [49, p.259].

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

    Blagoje Oblak

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Oblak, B. (2017). Partition Functions and Characters. In: BMS Particles in Three Dimensions. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-61878-4_11

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