Understand
It is shown that different couples of stress-energy and spin tensors of quantum relativistic fields, which would be otherwise equivalent, are in fact inequivalent if the second law of thermodynamics is taken into account.
- The proof of the inequivalence is based on the analysis of a macroscopic system at full thermodynamical equilibrium with a macroscopic total angular momentum and a specific instance is given for the free Dirac field, for which we show that the canonical and Belinfante stress-energy tensors are not equivalent.
- For this particular case, we show that the difference between the predicted angular momentum densities for a rotating system at full thermodynamical equilibrium is a quantum effect, persisting in the non-relativistic limit, corresponding to a polarization of particles of the order of \hbar \omega/KT (\omega being the angular velocity) and could in principle be measured experimentally.
- This result implies that specific stress-energy and spin tensors are physically meaningful even in the absence of gravitational coupling and raises the issue of finding the thermodynamically right (or the right class of) tensors.