A relativistic discrete spacetime formulation of 3+1 QED
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| author | Eon, Nathanaël Di Molfetta, Giuseppe Magnifico, Giuseppe Arrighi, Pablo |
| author_facet | Eon, Nathanaël Di Molfetta, Giuseppe Magnifico, Giuseppe Arrighi, Pablo |
| contents | This work provides a relativistic, digital quantum simulation scheme for both $2+1$ and $3+1$ dimensional quantum electrodynamics (QED), based on a discrete spacetime formulation of theory. It takes the form of a quantum circuit, infinitely repeating across space and time, parametrised by the discretization step $Δ_t=Δ_x$. Strict causality at each step is ensured as circuit wires coincide with the lightlike worldlines of QED; simulation time under decoherence is optimized. The construction replays the logic that leads to the QED Lagrangian. Namely, it starts from the Dirac quantum walk, well-known to converge towards free relativistic fermions. It then extends the quantum walk into a multi-particle sector quantum cellular automata in a way which respects the fermionic anti-commutation relations and the discrete gauge invariance symmetry. Both requirements can only be achieved at cost of introducing the gauge field. Lastly the gauge field is given its own electromagnetic dynamics, which can be formulated as a quantum walk at each plaquette. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_03148 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A relativistic discrete spacetime formulation of 3+1 QED Eon, Nathanaël Di Molfetta, Giuseppe Magnifico, Giuseppe Arrighi, Pablo Quantum Physics Formal Languages and Automata Theory Cellular Automata and Lattice Gases This work provides a relativistic, digital quantum simulation scheme for both $2+1$ and $3+1$ dimensional quantum electrodynamics (QED), based on a discrete spacetime formulation of theory. It takes the form of a quantum circuit, infinitely repeating across space and time, parametrised by the discretization step $Δ_t=Δ_x$. Strict causality at each step is ensured as circuit wires coincide with the lightlike worldlines of QED; simulation time under decoherence is optimized. The construction replays the logic that leads to the QED Lagrangian. Namely, it starts from the Dirac quantum walk, well-known to converge towards free relativistic fermions. It then extends the quantum walk into a multi-particle sector quantum cellular automata in a way which respects the fermionic anti-commutation relations and the discrete gauge invariance symmetry. Both requirements can only be achieved at cost of introducing the gauge field. Lastly the gauge field is given its own electromagnetic dynamics, which can be formulated as a quantum walk at each plaquette. |
| title | A relativistic discrete spacetime formulation of 3+1 QED |
| topic | Quantum Physics Formal Languages and Automata Theory Cellular Automata and Lattice Gases |
| url | https://arxiv.org/abs/2205.03148 |