  Ambiguities in the definition of angular momentum of a quantum-mechanical
particle in the presence of a magnetic vortex are reviewed. We show that the
long-standing problem of the adequate definition is resolved in the framework
of the second-quantized theory at nonzero temperature. Planar relativistic
Fermi gas in the background of a point-like magnetic vortex with arbitrary flux
is considered, and we find thermal averages, quadratic fluctuations, and
correlations of all observables, including angular momentum, in this system.
The kinetic definition of angular momentum is picked out unambiguously by the
requirement of plausible behaviour for the angular momentum fluctuation and its
correlation with fermion number.
