# Model for the propagation of fermions in a Bose-Einstein condensate

## TL;DR

This paper develops a model to analyze how fermions propagate within a Bose-Einstein condensate, deriving their dispersion relations and interaction effects, with potential implications for neutrino physics.

## Contribution

It introduces a method to explicitly compute fermion dispersion relations in a BEC and assesses interaction corrections, extending previous models.

## Key findings

- Dispersion relations are explicitly derived for fermions in a BEC.
- Interaction effects cause measurable corrections to fermion dispersion.
- Potential applications to neutrino behavior in condensate environments.

## Abstract

We consider the dispersion relations of fermions that propagate in the background of a scalar Bose-Einstein condensate. Some illustrative examples are discussed using simple Yukawa-type coupling models between the fermions and the scalar fields. The dispersion relations are determined explicitly in those cases, to the lowest order. The method also allows to determine the corrections to the dispersion relations due to the interactions with the excitations of the Bose-Einstein condensate. Possible applications of the results to the case of neutrinos are indicated.