  The macroscopic energy-momentum and spin densities of relativistic spin
hydrodynamics are obtained from the ensemble average of their respective
microscopic definitions (quantum operators). These microscopic definitions
suffer from ambiguities, meaning that, one may obtain different forms of
symmetric energy-momentum tensor and spin tensor through pseudogauge
transformations (or in other words Belinfante improvement procedure). However,
this ambiguity can be removed if we obtain these currents using Noether's
second theorem instead of widely used Noether's first theorem. In this article,
we use Noether's second theorem to derive energy-momentum and spin currents
without the need of pseudogauge transformations for free Dirac massive
particles with spin one-half.
