  Physical problems for which the existence of non-trivial topological Pauli
phase (i.e. fractional quantization of angular orbital angular momenta that is
possible in 2D case) is essential are discussed within the framework of
two-dimensional Helmholtz, Schroedinger and Dirac equations.
  As examples in classical field theory we consider a "wedge problem" -- a
description of a field generated by a point charge between two conducting
half-planes -- and a Fresnel diffraction from knife-edge.
  In few-electron circular quantum dots the choice between integer and
half-integer quantization of orbital angular momenta is defined by the Pauli
principle. This is in line with precise experimental data for the ground state
energy of such quantum dots in a perpendicular magnetic field.
  In a gapless graphene, as in the case of gapped one, in the presence of
overcharged impurity this problem can be solved experimentally, e.g., using the
method of scanning tunnel spectroscopy.
