The Dirac Vacuum in Discrete Spacetime

• URL: http://arxiv.org/abs/2412.03466v3
• Date: Fri, 29 Aug 2025 14:53:39 GMT
• Title: The Dirac Vacuum in Discrete Spacetime
• Abstract summary: We consider introducing the Dirac sea in a quantum cellular automata model of fermions in discrete spacetime.<n>A new boundary is created between positive and negative energy states, at which pair creation seems energetically favourable.<n>This happens because of the modular nature of energy in discrete time models.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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