The Dirac Vacuum in Discrete Spacetime

TL;DR

This paper explores incorporating the Dirac vacuum into a discrete spacetime quantum cellular automaton model, highlighting challenges with negative energy states and proposing modifications to address pair creation issues.

Contribution

It introduces a novel approach to modeling the Dirac vacuum in discrete spacetime automata and proposes a method to mitigate boundary-related pair creation problems.

Findings

Identifies a boundary issue between positive and negative energy states in the model.

Shows that the modular energy structure causes pair creation at the boundary.

Suggests amendments to the model to prevent states from approaching the boundary.

Abstract

We consider introducing the Dirac sea in a quantum cellular automata model of fermions in discrete spacetime which approximates the Dirac equation in the continuum limit. However, if we attempt to fill up the `negative' energy states, we run into a problem. A new boundary is created between positive and negative energy states, at which pair creation seems energetically favourable. This happens because of the modular nature of energy in discrete time models. We then suggest a possible remedy by amending the model, in order to pull states away from the new boundary.