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Coherent state path integrals are applied to a many-body problem fornon-relativistic electrons in a central potential and an external magneticfield; however, in comparison to previous coherent state path integrals, wedefinitely fix the symmetry quantum numbers to specific values with secondquantized field operators which are restricted by delta functions of a Diracidentity in a trace representation of anti-commuting coherent states. Weperform an anomalous doubling for the delta functions of the two-particle partsso that a Hubbard-Stratonovich transformation can be taken for correspondingself-energies with a coset decomposition. The given field theory can beextended to an ensemble average over the external magnetic field so that meaneigenvalue densities and eigenvalue correlations can be obtained.

Field theory with coherent states for many-body problems with specified  particle- and symmetry- quantum numbers (Non-relativistic electrons in a  central potential and an external magnetic field)