# Gauss's law, the manifestations of gauge fields, and their impact on local observables

December 21, 2022

Within the framework of the universal algebra of the electromagnetic field,
the impact of globally neutral configurations of external charges on the field
is analyzed. External charges are not affected by the field, but they induce
localized automorphisms of the universal algebra. Gauss's law implies that
these automorphisms cannot be implemented by unitary operators involving only
the electromagnetic field, they are outer automorphisms. The missing degrees of
freedom can be incorporated in an enlargement of the universal algebra, which
can concretely be represented by exponential functions of gauge fields and an
abelian algebra describing the external charges. In this manner, gauge fields
manifest themselves in the framework of gauge invariant observables. The action
of the automorphisms on the vacuum state gives rise to representations of the
electromagnetic field with vanishing global charge, which are locally disjoint
from the vacuum representation. This feature disappears in the enlarged
universal algebra of the electromagnetic field. The energy content of the
states is well defined in both cases and bounded from below. The passage from
these globally neutral states to charged states and the determination of their
energy content are also being discussed.

Keywords:

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