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

October 04, 2016

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.

Keywords:

*none*