The Dirac Vacuum in Discrete Spacetime

Chaitanya Gupta; A J  Short

doi:10.22331/q-2025-09-03-1845

The Dirac Vacuum in Discrete Spacetime

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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.

Original language	English
Article number	1845
Pages (from-to)	1-15
Number of pages	15
Journal	Quantum
Volume	9
DOIs	https://doi.org/10.22331/q-2025-09-03-1845
Publication status	Published - 3 Sept 2025

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Publisher Copyright:
© Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. Some rights reserved.

Keywords

Quantum Cellular Automata
Quantum walk
Dirac Vacuum
Dirac Sea

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title = "The Dirac Vacuum in Discrete Spacetime",

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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AU - Gupta, Chaitanya

AU - Short, A J

N1 - Publisher Copyright: © Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. Some rights reserved.

PY - 2025/9/3

Y1 - 2025/9/3

N2 - 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.

AB - 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.

KW - Quantum Cellular Automata

KW - Quantum walk

KW - Dirac Vacuum

KW - Dirac Sea

U2 - 10.22331/q-2025-09-03-1845

DO - 10.22331/q-2025-09-03-1845

M3 - Article (Academic Journal)

SN - 2521-327X

VL - 9

SP - 1

EP - 15

JO - Quantum

JF - Quantum

M1 - 1845

ER -

The Dirac Vacuum in Discrete Spacetime

Abstract

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Keywords

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