Free Fermions on causal sets

TL;DR

This paper develops a Dirac theory for free fermions on causal sets, emphasizing the emergent nature of causets and introducing mixed norm spaces that accommodate negative norm particles and ghosts.

Contribution

It introduces a novel Dirac theory on causal sets incorporating mixed norm spaces, enabling the treatment of negative norm particles and ghosts.

Findings

Successful construction of a Dirac theory on causal sets.

Identification of mixed norm spaces in the framework.

Recognition of negative norm particles and ghosts in the model.

Abstract

We construct a Dirac theory on causal sets; a key element in the construction being that the causet must be regarded as emergent in an appropriate sense too. We further notice that mixed norm spaces appear in the construction allowing for negative norm particles and "ghosts".