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The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields

Dedicated to Karl-Henning Rehren on the occasion of his 60th birthday

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Abstract

Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial topological charges, described by pairs of fields localised in certain topologically non-trivial spacelike separated regions, can appear in regular representations of the algebra only if the fields depend non-linearly on the mollifying test functions. On the other hand, examples of regular vacuum representations with non-trivial topological charges are constructed, where the underlying field still satisfies a weakened form of “spacelike linearity”. Such representations also appear in the presence of electric currents. The status of topological charges in theories with several types of electromagnetic fields, which appear in the short distance (scaling) limit of asymptotically free non-abelian gauge theories, is also briefly discussed.

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Acknowledgements

DB gratefully acknowledges the hospitality and financial support extended to him by the University of Rome “Tor Vergata” which made this collaboration possible. FC and GR are supported by the ERC Advanced Grant 669240 QUEST “Quantum Algebraic Structures and Models”. EV is supported in part by OPAL “Consolidate the Foundations”.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany

    Detlev Buchholz

  2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy

    Fabio Ciolli, Giuseppe Ruzzi & Ezio Vasselli

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  1. Detlev Buchholz
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  2. Fabio Ciolli
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  3. Giuseppe Ruzzi
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  4. Ezio Vasselli
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Correspondence to Detlev Buchholz.

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Buchholz, D., Ciolli, F., Ruzzi, G. et al. The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields. Lett Math Phys 107, 201–222 (2017). https://doi.org/10.1007/s11005-016-0931-x

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  • DOI: https://doi.org/10.1007/s11005-016-0931-x

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