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Buchholz, Detlev; Ciolli, Fabio; Ruzzi, Giuseppe; Vasselli, Ezio

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. (English) Zbl 1364.81238

Lett. Math. Phys. 107, No. 2, 201-222 (2017).
Summary: 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.
For Part I see [the authors, ibid. 106, No. 2, 269–285 (2016; Zbl 1330.81201)].

Cited in 1 Review
Cited in 6 Documents

MSC:

81V10 Electromagnetic interaction; quantum electrodynamics
81T05 Axiomatic quantum field theory; operator algebras
14F40 de Rham cohomology and algebraic geometry
46L05 General theory of \(C^*\)-algebras
46L60 Applications of selfadjoint operator algebras to physics

Keywords:

electromagnetic field; topological charges; non-linear field operators

Biographic References:

Rehren, Karl-Henning

Citations:

Zbl 1330.81201
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Full Text: DOI arXiv

References:

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