A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits
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 partic...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2022-02-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-022-06241-4 |
| _version_ | 1818330678493708288 |
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| author | Kevissen Sellapillay Pablo Arrighi Giuseppe Di Molfetta |
| author_facet | Kevissen Sellapillay Pablo Arrighi Giuseppe Di Molfetta |
| author_sort | Kevissen Sellapillay |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T13:07:46Z |
| format | Article |
| id | doaj.art-b0ce3c227cce42bc8713439ba3a6198d |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-12-13T13:07:46Z |
| publishDate | 2022-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-b0ce3c227cce42bc8713439ba3a6198d2022-12-21T23:44:47ZengNature PortfolioScientific Reports2045-23222022-02-011211910.1038/s41598-022-06241-4A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limitsKevissen Sellapillay0Pablo Arrighi1Giuseppe Di Molfetta2Aix-Marseille Université, CPTUniversité Paris-Saclay, CNRS, Laboratoire de recherche en informatiqueAix-Marseille Université, Université de Toulon, CNRS, LISAbstract 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.https://doi.org/10.1038/s41598-022-06241-4 |
| spellingShingle | Kevissen Sellapillay Pablo Arrighi Giuseppe Di Molfetta A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits Scientific Reports |
| title | A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits |
| title_full | A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits |
| title_fullStr | A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits |
| title_full_unstemmed | A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits |
| title_short | A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits |
| title_sort | discrete relativistic spacetime formalism for 1 1 qed with continuum limits |
| url | https://doi.org/10.1038/s41598-022-06241-4 |
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