Journal Article

PUBDB-2023-04846

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Canonical momenta in digitized Su(2) lattice gauge theory: definition and free theory

Jakobs, T. ; Garofalo, M. ; Hartung, T. ; Jansen, K.DESY* ; Ostmeyer, J. ; Rolfes, D. ; Romiti, S. ; Urbach, C. (Corresponding author)

2023
Springer Heidelberg

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Please use a persistent id in citations: doi:10.1140/epjc/s10052-023-11829-9  doi:10.3204/PUBDB-2023-04846

Report No.: arXiv:2304.02322

Abstract: Hamiltonian simulations of quantum systems require a finite-dimensional representation of the operators acting on the Hilbert space $\mathcal {H}$. 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 $\mathcal {H}$. This is achieved by discretising the sphere $S_3$ 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 $S_3$ 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.

Keyword(s): gauge field theory: SU(2) ; operator: Casimir ; effect: discrete ; commutation relations ; sphere ; Hilbert space ; lattice field theory ; lattice ; operator: Laplace ; Hamiltonian

Note: typos corrected, matches published version in EPJC

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Contributing Institute(s):

1. Centre f. Quantum Techno. a. Application (CQTA)
2. Zeuthen Particle PhysicsTheory (Z_ZPPT)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2023

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Database coverage:
; ; ; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; DOAJ Seal ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; SCOAP3 sponsored Journal ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint Jakobs, T. ; Garofalo, M. ; Hartung, T. ; Jansen, K.DESY* ; Ostmeyer, J. ; Rolfes, D. ; Romiti, S. ; Urbach, C. (Collaboration author)Extern*
Canonical Momenta in Digitized SU(2) Lattice Gauge Theory: Definition and Free Theory
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