A single-particle framework for unitary lattice gauge theory in discrete time
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912753639227392 |
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| author | Arnault, Pablo Cedzich, Christopher |
| author_facet | Arnault, Pablo Cedzich, Christopher |
| contents | We construct a real-time lattice-gauge-theory-type action for a spin-1/2 matter field of a single particle on a (1+1)-dimensional spacetime lattice. The framework is based on a discrete-time quantum walk, and is hence inherently unitary and strictly local, i.e., transition amplitudes exactly vanish outside of a lightcone on the lattice. We then provide a lattice Noether's theorem for internal symmetries of this action. We further couple this action to an electromagnetic field by a minimal substitution on the lattice. Finally, we suggest a real-time lattice-gauge-theory-type action for the electromagnetic field in arbitrary spacetime dimensions, and derive its classical equations of motion, which are lattice versions of Maxwell's equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_14997 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A single-particle framework for unitary lattice gauge theory in discrete time Arnault, Pablo Cedzich, Christopher Quantum Physics Other Condensed Matter High Energy Physics - Lattice We construct a real-time lattice-gauge-theory-type action for a spin-1/2 matter field of a single particle on a (1+1)-dimensional spacetime lattice. The framework is based on a discrete-time quantum walk, and is hence inherently unitary and strictly local, i.e., transition amplitudes exactly vanish outside of a lightcone on the lattice. We then provide a lattice Noether's theorem for internal symmetries of this action. We further couple this action to an electromagnetic field by a minimal substitution on the lattice. Finally, we suggest a real-time lattice-gauge-theory-type action for the electromagnetic field in arbitrary spacetime dimensions, and derive its classical equations of motion, which are lattice versions of Maxwell's equations. |
| title | A single-particle framework for unitary lattice gauge theory in discrete time |
| topic | Quantum Physics Other Condensed Matter High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2208.14997 |