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)

TL;DR

This paper develops a coherent state path integral approach for many-body non-relativistic electrons in a central potential and magnetic field, explicitly fixing symmetry quantum numbers and enabling analysis of eigenvalue statistics.

Contribution

It introduces a method to fix symmetry quantum numbers in coherent state path integrals for many-body systems, extending the approach to include ensemble averages over magnetic fields.

Findings

Fixed symmetry quantum numbers using delta functions in path integrals.

Enabled calculation of eigenvalue densities and correlations.

Extended the theory to ensemble averages over magnetic fields.

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.