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)

Abstract

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.