Exotic fermionic fields and minimal length

TL;DR

This paper explores how minimal length effects and exotic spinors influence the Dirac equation, revealing that exotic spinors enable non-trivial solutions in scenarios where minimal length alone restricts solutions.

Contribution

It combines minimal length and exotic spinor frameworks to analyze their impact on fermionic equations, highlighting the unique role of exotic spinors in allowing non-trivial solutions.

Findings

Minimal length leads to only trivial solutions for free fermions.

Exotic spinors prevent the Dirac operator from being injective.

Exoticity allows non-trivial solutions despite minimal length constraints.

Abstract

We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle, and exotic spinors, associated with any non-trivial topology equipping the spacetime manifold. We show that the free fermionic dynamical equations, within the context of a minimal length, just allow for trivial solutions, a feature that is not shared by dynamical equations for exotic spinors. In fact, in this coalescing setup, the exoticity is shown to prevent the Dirac operator to be injective, allowing the existence of non-trivial solutions.