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Journal Articles Scientific Reports Year : 2022

## A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits

Di Molfetta Giuseppe
Kevissen Sellapillay
• Function : Author
Pablo Arrighi
• Function : Author
Giuseppe Di Molfetta
• Function : Author

#### Abstract

Abstract We build a quantum cellular automaton (QCA) which coincides with $1+1$ 1 + 1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with the gauge field on the links. The particles are massive fermions, and the evolution is exactly U (1) gauge-invariant. We show that, in the continuous-time discrete-space limit, the QCA converges to the Kogut–Susskind staggered version of $1+1$ 1 + 1 QED. We also show that, in the continuous spacetime limit and in the free one particle sector, it converges to the Dirac equation—a strong indication that the model remains accurate in the relativistic regime.

#### Domains

Physics [physics] Quantum Physics [quant-ph]

### Dates and versions

hal-03594721 , version 1 (02-03-2022)

### Identifiers

• HAL Id : hal-03594721 , version 1
• DOI :
• PUBMEDCENTRAL :

### Cite

Di Molfetta Giuseppe, Kevissen Sellapillay, Pablo Arrighi, Giuseppe Di Molfetta. A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits. Scientific Reports, 2022, 12 (1), pp.2198. ⟨10.1038/s41598-022-06241-4⟩. ⟨hal-03594721⟩

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