Emergent relativistic-like Kinematics and Dynamical Mass Generation for a Lifshitz-type Yukawa model

TL;DR

This paper investigates how a Lifshitz-type Yukawa model exhibits emergent relativistic dispersion relations and dynamical mass generation in the IR regime, with particles remaining massive and subluminal.

Contribution

It demonstrates the dynamical emergence of relativistic-like kinematics and mass generation in a Lifshitz-type Yukawa model, extending understanding of IR behavior in such theories.

Findings

Relativistic-like dispersion relations emerge in the IR after quantum corrections.

Particles acquire dynamical masses even with zero bare masses.

Massive particles have group velocities below the speed of light.

Abstract

We study the Infra Red (IR) limit of dispersion relations for scalar and fermion fields in a Lifshitz-type Yukawa model, after dressing by quantum fluctuations. Relativistic-like dispersion relations emerge dynamically in the IR regime of the model, after quantum corrections are taken into account. In this regime, dynamical mass generation also takes place, but in such a way that the particle excitations remain massive, even if the bare masses vanish. The group velocities of the corresponding massive particles of course are smaller than the speed of light, in a way consistent with the IR regime where the analysis is performed. We also comment on possible extensions of the model where the fermions are coupled to an Abelian gauge field.