Eur. Phys. J. C (2020) 80: 727
https://doi.org/10.1140/epjc/s10052-020-8313-z

Regular Article - Theoretical Physics

Exotic fermionic fields and minimal length

¹ Departamento de Física, Universidade Estadual Paulista, UNESP, Av. Dr. Ariberto Pereira da Cunha, 333, Guaratinguetá, SP, Brazil
² Instituto Federal de Educação, Ciência e Tecnologia do Norte de Minas Gerais, IFNMG, Av. Dr. Humberto Mallard, 1355, Pirapora, MG, Brazil
³ CMCC, Federal University of ABC, 09210-580, Santo André, Brazil

^* e-mail: julio.hoff@unesp.br

Received: 5 June 2020
Accepted: 30 July 2020
Published online: 12 August 2020

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.