Coherent state path integral and nonlinear sigma model for a condensate composed of fermions with precise, discrete steps in the time development

TL;DR

This paper develops an exact nonlinear sigma model for fermionic condensates using a coherent state path integral with precise discrete time steps, addressing a common issue in quantum many-body physics.

Contribution

It introduces a detailed derivation of a nonlinear sigma model for fermion pair condensates that accounts for exact discrete time steps, improving upon previous approximate methods.

Findings

Exact treatment of spontaneous symmetry breaking in fermionic systems

Inclusion of precise discrete time steps in path integral formulation

Enhanced modeling of fermion pair condensates

Abstract

A coherent state path integral is considered for fermions with precise, discrete time separation. We derive in detail a nonlinear sigma model of a pair condensate concerning the precise, discrete time step order which is usually abbreviated by the appealing (but in fact non-existent) hermitian form of the fields. This problem is ubiquitous in quantum many-body physics and already occurs in the original Dyson equation. However, one has only to include a few amendments concerning the precise, discrete time step development of coherent state path integrals, compared to previous, abridged approaches, so that one can accomplish the exact treatment of a spontaneous symmetry breaking with a coset decomposition for pair condensates and density parts.