  Massive QED, in contrast with its massless counterpart, possesses two
conserved charges; one is a screened (vanishing) Maxwell charge which is
directly associated with the massive vector mesons through the identically
conserved Maxwell current. A somewhat peculiar situation arises for couplings
of Hermitian matter fields to massive vector potentials; in that case the only
current is the screened Maxwell current and the coupling disappears in the
massless limit. In case of selfinteracting massive vector mesons the situation
becomes even more peculiar in that the usually renormalizability guaranteeing
validity of the first order power-counting criterion breaks down in second
order and requires the compensatory presence of additional Hermitian H-fields.
Some aspect of these observation have already been noticed in the BRST gauge
theoretic formulation, but here we use a new setting based on string-local
vector mesons which is required by Hilbert space positivity. The coupling to
H-fields induces Mexican hat like selfinteractions; they are not imposed and
bear no relation with spontaneous symmetry breaking; they are rather
consequences of the foundational causal localization properties realized in a
Hilbert space setting. In case of selfinteracting massive vectormesons their
presence is required in order to maintain the first order power-counting
restriction of renormalizability also in second order. The presentation of the
new Hilbert space setting for vector mesons which replaces gauge theory and
extends on-shell unitarity to its off-shell counterpart is the main motivation
for this work. The new Hilbert space setting also shows that the second order
Lie-algebra structure of selfinteracting vector mesons is a consequence of the
principles of QFT and promises a deeper understanding of the origin of
confinement.
