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Quantum Spacetime and Algebraic Quantum Field Theory

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Advances in Algebraic Quantum Field Theory

Part of the book series: Mathematical Physics Studies ((MPST))

Abstract

We review the investigations on the quantum structure of spacetime, to be found at the Planck scale if one takes into account the operational limitations to the localization of events which result from the concurrence of Quantum Mechanics and General Relativity. We also discuss the different approaches to (perturbative) Quantum Field Theory on Quantum Spacetime, and some of the possible cosmological consequences.

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Notes

  1. 1.

    Of course \(\mathcal K^{\otimes n}\simeq \mathcal K\), so that \(\mathscr {E}^{(n)}\simeq \mathscr {E}\).

  2. 2.

    Such a limitation could not be obtained in any case if coordinates have to be represented by selfadjoint operators, unless the availability of (generalized) eigenstates is restricted.

  3. 3.

    This set is nonempty, as the Gauss function is the Wigner function of the best localized states.

  4. 4.

    Note however, that in a Euclidean realm at least, there is hope that an infrared-cutoff model, the so-called Grosse-Wulkenhaar model might have a chance to be resummable and thus give way even to a constructible theory.

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Authors and Affiliations

  1. Mathematisches Institut and Courant Research Centre “Higher Order Structures in Mathematics”, Universität Göttingen, Bunsenstr. 3-5, D-37073, Göttingen, Germany

    Dorothea Bahns

  2. Dipartimento di Matematica, Università di Roma “La Sapienza”, P.le Aldo Moro, 5, I-00185, Roma, Italy

    Sergio Doplicher

  3. Dipartimento di Matematica, Università di Roma Tor Vergata, V.le Della Ricerca Scientifica, 1, I-00133, Roma, Italy

    Gerardo Morsella

  4. SISSA, Via Bonomea, 265, I-34136, Trieste, Italy

    Gherardo Piacitelli

Authors
  1. Dorothea Bahns
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  2. Sergio Doplicher
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  3. Gerardo Morsella
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  4. Gherardo Piacitelli
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Corresponding author

Correspondence to Gerardo Morsella .

Editor information

Editors and Affiliations

  1. University of Trento, Trento, Italy

    Romeo Brunetti

  2. University of Pavia, Pavia, Italy

    Claudio Dappiaggi

  3. University of Hamburg, Hamburg, Germany

    Klaus Fredenhagen

  4. University of Vienna, Vienna, Austria

    Jakob Yngvason

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Bahns, D., Doplicher, S., Morsella, G., Piacitelli, G. (2015). Quantum Spacetime and Algebraic Quantum Field Theory. In: Brunetti, R., Dappiaggi, C., Fredenhagen, K., Yngvason, J. (eds) Advances in Algebraic Quantum Field Theory. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-21353-8_7

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