Canonical momenta in digitized Su(2) lattice gauge theory: definition and free theory
Abstract Hamiltonian simulations of quantum systems require a finite-dimensional representation of the operators acting on the Hilbert space $$\mathcal {H}$$ H . Here we give a prescription for gauge links and canonical momenta of an SU(2) gauge theory, such that the matrix representation of the for...
| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-07-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-023-11829-9 |
| _version_ | 1797689133009731584 |
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| author | Timo Jakobs Marco Garofalo Tobias Hartung Karl Jansen Johann Ostmeyer Dominik Rolfes Simone Romiti Carsten Urbach |
| author_facet | Timo Jakobs Marco Garofalo Tobias Hartung Karl Jansen Johann Ostmeyer Dominik Rolfes Simone Romiti Carsten Urbach |
| author_sort | Timo Jakobs |
| collection | DOAJ |
| description | Abstract Hamiltonian simulations of quantum systems require a finite-dimensional representation of the operators acting on the Hilbert space $$\mathcal {H}$$ H . Here we give a prescription for gauge links and canonical momenta of an SU(2) gauge theory, such that the matrix representation of the former is diagonal in $$\mathcal {H}$$ H . This is achieved by discretising the sphere $$S_3$$ S 3 isomorphic to SU(2) and the corresponding directional derivatives. We show that the fundamental commutation relations are fulfilled up to discretisation artefacts. Moreover, we directly construct the Casimir operator corresponding to the Laplace–Beltrami operator on $$S_3$$ S 3 and show that the spectrum of the free theory is reproduced again up to discretisation effects. Qualitatively, these results do not depend on the specific discretisation of SU(2), but the actual convergence rates do. |
| first_indexed | 2024-03-12T01:41:35Z |
| format | Article |
| id | doaj.art-8a8cf5db2dfd4835af1a2a5afb6db076 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-03-12T01:41:35Z |
| publishDate | 2023-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-8a8cf5db2dfd4835af1a2a5afb6db0762023-09-10T11:23:05ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-07-0183711910.1140/epjc/s10052-023-11829-9Canonical momenta in digitized Su(2) lattice gauge theory: definition and free theoryTimo Jakobs0Marco Garofalo1Tobias Hartung2Karl Jansen3Johann Ostmeyer4Dominik Rolfes5Simone Romiti6Carsten Urbach7Helmholtz-Institut für Strahlen- und Kernphysik, University of BonnHelmholtz-Institut für Strahlen- und Kernphysik, University of BonnNortheastern University-LondonCQTA, DESY ZeuthenDepartment of Mathematical Sciences, University of LiverpoolHelmholtz-Institut für Strahlen- und Kernphysik, University of BonnHelmholtz-Institut für Strahlen- und Kernphysik, University of BonnHelmholtz-Institut für Strahlen- und Kernphysik, University of BonnAbstract Hamiltonian simulations of quantum systems require a finite-dimensional representation of the operators acting on the Hilbert space $$\mathcal {H}$$ H . Here we give a prescription for gauge links and canonical momenta of an SU(2) gauge theory, such that the matrix representation of the former is diagonal in $$\mathcal {H}$$ H . This is achieved by discretising the sphere $$S_3$$ S 3 isomorphic to SU(2) and the corresponding directional derivatives. We show that the fundamental commutation relations are fulfilled up to discretisation artefacts. Moreover, we directly construct the Casimir operator corresponding to the Laplace–Beltrami operator on $$S_3$$ S 3 and show that the spectrum of the free theory is reproduced again up to discretisation effects. Qualitatively, these results do not depend on the specific discretisation of SU(2), but the actual convergence rates do.https://doi.org/10.1140/epjc/s10052-023-11829-9 |
| spellingShingle | Timo Jakobs Marco Garofalo Tobias Hartung Karl Jansen Johann Ostmeyer Dominik Rolfes Simone Romiti Carsten Urbach Canonical momenta in digitized Su(2) lattice gauge theory: definition and free theory European Physical Journal C: Particles and Fields |
| title | Canonical momenta in digitized Su(2) lattice gauge theory: definition and free theory |
| title_full | Canonical momenta in digitized Su(2) lattice gauge theory: definition and free theory |
| title_fullStr | Canonical momenta in digitized Su(2) lattice gauge theory: definition and free theory |
| title_full_unstemmed | Canonical momenta in digitized Su(2) lattice gauge theory: definition and free theory |
| title_short | Canonical momenta in digitized Su(2) lattice gauge theory: definition and free theory |
| title_sort | canonical momenta in digitized su 2 lattice gauge theory definition and free theory |
| url | https://doi.org/10.1140/epjc/s10052-023-11829-9 |
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