  Coherent state path integrals are applied to a many-body problem for
non-relativistic electrons in a central potential and an external magnetic
field; however, in comparison to previous coherent state path integrals, we
definitely fix the symmetry quantum numbers to specific values with second
quantized field operators which are restricted by delta functions of a Dirac
identity in a trace representation of anti-commuting coherent states. We
perform an anomalous doubling for the delta functions of the two-particle parts
so that a Hubbard-Stratonovich transformation can be taken for corresponding
self-energies with a coset decomposition. The given field theory can be
extended to an ensemble average over the external magnetic field so that mean
eigenvalue densities and eigenvalue correlations can be obtained.
