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Invitation: Gravity, Point Particles, and Group-Valued Momenta

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Deformations of Spacetime Symmetries

Part of the book series: Lecture Notes in Physics ((LNP,volume 986))

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Abstract

The growth of our understanding of physics of the fundamental constituents of matter in the last century is truly remarkable. Hundred years ago, general relativity had been just formulated, and the researchers still had to wait to witness the dawn of quantum mechanics, to mention only these two major theories that shaped the development of physics ever since.

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Notes

  1. 1.

    Since the value of the deformation parameter is to be derived from some fundamental theory and/or experiments, in what follows we will use \(\kappa \) to denote the deformation parameter, whose value is not fixed, while the term ‘Planck mass’ will refer to \(M_{Pl} =\sqrt{\hslash /G} \sim 10^{19}\) GeV.

  2. 2.

    In the recent years, Born’s ideas found their new incarnations in investigations of new mathematical structures in symplectic geometry (see [30] and references therein) and in a new model in string theory, called the metastring theory [31,32,33,34,35].

  3. 3.

    As cited in [38].

  4. 4.

    In this book, we use the units in which \(c=1\).

  5. 5.

    It is worth noticing in passing that also in 3+1 dimensions the Einstein equations make the components of the Ricci tensor completely fixed by the distribution of matter. Therefore, all the dynamical degrees of freedom of gravity are captured by the Weyl tensor \(C_{\mu \nu \rho \sigma }\).

  6. 6.

    We will consider spinning particles in the next chapter. Let us remark here that a non-vanishing spin of the point particle is associated to a time-offset in the conical geometry. See, e.g., [47] for details.

  7. 7.

    For the technical details about the procedure of boosting a conical defect, see [45].

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Authors and Affiliations

  1. Department of Physics, University of Naples Federico II, Naples, Italy

    Michele Arzano

  2. Institute for Theoretical Physics, University of Wrocław, Wroclaw, Poland

    Jerzy Kowalski-Glikman

  3. National Centre for Nuclear Research, Swierk, Poland

    Jerzy Kowalski-Glikman

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Arzano, M., Kowalski-Glikman, J. (2021). Invitation: Gravity, Point Particles, and Group-Valued Momenta. In: Deformations of Spacetime Symmetries. Lecture Notes in Physics, vol 986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-63097-6_1

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