Abstract:
Two formulations of relativistic hydrodynamics of particles with spin 1/2 are compared. The first approach,
dubbed the canonical one, uses expressions for the energy-momentum and spin tensors that have properties
that follow a direct application of Noether’s theorem, which yields a totally antisymmetric spin tensor. The
other one is based on a simplified form of the spin tensor and is commonly used in the current literature
under the name of a phenomenological approach. We show that these two frameworks are equivalent, i.e.,
they can be directly connected by a suitably defined pseudogauge transformation, only if the first framework
is initially improved by a suitable modification of the energy-momentum tensor (addition of a divergence-free
term that cannot be interpreted as a pseudogauge). Our analysis uses arguments related to the positivity of
entropy production. The latter turns out to be equivalent for the improved canonical and phenomenological
frameworks