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.

Buchholz, D., Ciolli, F., Ruzzi, G., Vasselli, E. (2017). The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields. LETTERS IN MATHEMATICAL PHYSICS, 107(2), 201-222 [10.1007/s11005-016-0931-x].

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

Ciolli F.;Ruzzi G.;
2017-01-01

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.
2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
Settore MAT/07 - FISICA MATEMATICA
English
Con Impact Factor ISI
Electromagnetic field; Non-linear field operators; Topological charges
http://www.kluweronline.com/issn/0377-9017
Buchholz, D., Ciolli, F., Ruzzi, G., Vasselli, E. (2017). The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields. LETTERS IN MATHEMATICAL PHYSICS, 107(2), 201-222 [10.1007/s11005-016-0931-x].
Buchholz, D; Ciolli, F; Ruzzi, G; Vasselli, E
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/219499
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