  We investigate the properties of multi-particle states in Deformed Special
Relativity (DSR). Starting from the Lagrangian formalism with an energy
dependent metric, the conserved Noether current can be derived which is
additive in the usual way. The integrated Noether current had previously been
discarded as a conserved quantity, because it was correctly realized that it
does no longer obey the DSR transformations. We identify the reason for this
mismatch in the fact that DSR depends only on the extensive quantity of total
four-momentum instead of the energy-momentum densities as would be appropriate
for a field theory. We argue that the reason for the failure of DSR to
reproduce the standard transformation behavior in the well established limits
is due to the missing sensitivity to the volume inside which energy is
accumulated. We show that the soccer-ball problem is absent if one formulates
DSR instead for the field densities. As a consequence, estimates for predicted
effects have to be corrected by many orders of magnitude. Further, we derive
that the modified quantum field theory implies a locality bound.
