Resumo
Massive QED, in contrast with its massless counterpart, possesses two conserved charges; one isa screened (vanishing) Maxwell charge which is directly associated with the massive vector mesonsthrough the identically conserved Maxwell current, while the presence of a particle-antiparticle count-ing charge depends on the matter . A somewhat peculiar situation arises for couplings of Hermitianmatter fields to massive vector potentials; in that case the only current is the screened Maxwell currentand the coupling disappears in the massless limit.In case of selfinteracting massive vector mesons the situation becomes even more peculiar in thatthe usually renormalizability guaranteeing validity of the first order power-counting criterion breaksdown 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 formu-lation, but here we use a new setting based on string-local vector mesons which is required by Hilbertspace positivity (”off-shell unitarity”). This new formulation explains why spontaneous symmetrybreaking cannot occur in the presence of higher spin s ≥ 1 fields. The coupling to H-fields inducesMexican hat like selfinteractions; they are not imposed and bear no relation with spontaneous symme-try breaking; they are rather consequences of the foundational causal localization properties realizedin a Hilbert space setting. In case of selfinteracting massive vectormesons their presence is required inorder 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 andextends 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 selfinter-acting vector mesons is a consequence of the principles of QFT and promises a deeper understandingof the origin of confinement.