  This work aims to shed some light on the meaning of the positive energy
assumption in relativistic quantum theory and its relation to questions of
localization of quantum systems. It is shown that the positive energy property
of solutions of relativistic wave equations (such as the Dirac equation) is
very fragile with respect to state transformations beyond free time evolution.
Paying attention to the connection between negative energy Dirac wave functions
and pair creation processes in second quantization, this analysis leads to a
better understanding of a class of problems known as the localization problem
of relativistic quantum theory (associated for instance with famous results of
Newton and Wigner, Reeh and Schlieder, Hegerfeldt or Malament). Finally, this
analysis is reflected from the perspective of a Bohmian quantum field theory.
