# Supersymmetry representation of Bose-Einstein condensation of fermion pairs

## TL;DR

This paper develops a supersymmetry field theory framework to describe Bose-Einstein condensation in fermion pairs, revealing how supersymmetry breaking influences the emergence of condensates and fluctuations in Bose-Fermi mixtures.

## Contribution

It introduces a supersymmetry-based model for Bose-Fermi mixtures and derives new field equations describing the condensation process and fluctuation behavior.

## Key findings

- Fermion number conservation in supersymmetric degenerate mixtures.
- Supersymmetry breaking leads to specific field equations for real Bose-Fermi systems.
- Cooling induces inhomogeneous fluctuations and Bose condensate formation at lower temperatures.

## Abstract

We consider supersymmetry field theory with supercomponents being the square root of the Bose condensate density, the amplitude of its fluctuations and Grassmannian fields related to the Fermi particles density. The fermion number is demonstrated to be conserved in degenerated Fermi-Bose mixtures with unbroken supersymmetry when the system is invariant with respect to inversion of the time arrow. We show the supersymmetry breaking allows one to derive field equations describing behavior of real Bose-Fermi mixtures. Solution of related field equations reveals the cooling of homogeneously distributed fermions gives first spontaneous rise to strong inhomogeneous fluctuations, while the Bose condensate appears at a lower temperature dependent of the fermion density.