  This is the first in a series of papers on projective positive energy
representations of gauge groups. Let $\Xi \rightarrow M$ be a principal fiber
bundle, and let $\Gamma_{c}(M,\mathrm{Ad}(\Xi))$ be the group of compactly
supported (local) gauge transformations. If $P$ is a group of `space-time
symmetries' acting on $\Xi\rightarrow M$, then a projective unitary
representation of $\Gamma_{c}(M,\mathrm{Ad}(\Xi))\rtimes P$ is of positive
energy if every `timelike generator' $p_0 \in \mathfrak{p}$ gives rise to a
Hamiltonian $H(p_0)$ whose spectrum is bounded from below.
  Our main result shows that in the absence of fixed points for the cone of
timelike generators, the projective positive energy representations of the
connected component $\Gamma_{c}(M,\mathrm{Ad}(\Xi))_0$ come from 1-dimensional
$P$-orbits. For compact $M$ this yields a complete classification of the
projective positive energy representations in terms of lowest weight
representations of affine Kac-Moody algebras. For noncompact $M$, it yields a
classification under further restrictions on the space of ground states.
  In the second part of this series we consider larger groups of gauge
transformations, which contain also global transformations. The present results
are used to localize the positive energy representations at (conformal)
infinity.
