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

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• 作者：Detlev Buchholz ; Fabio Ciolli ; Giuseppe Ruzzi…
• 关键词：Electromagnetic field ; Topological charges ; Non ; linear field operators
• 刊名：Letters in Mathematical Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：107
• 期：2
• 页码：201-222
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Complex Systems; Geometry; Group Theory and Generalizations;
• 出版者：Springer Netherlands
• ISSN：1573-0530
• 卷排序：107

文摘

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.