https://doi.org/10.1140/epjc/s10052-024-13037-5
Regular Article - Theoretical Physics
Digitizing lattice gauge theories in the magnetic basis: reducing the breaking of the fundamental commutation relations
Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, University of Bonn, Bonn, Germany
a
simone.romiti.1994@gmail.com
Received:
7
December
2023
Accepted:
22
June
2024
Published online:
17
July
2024
We present a digitization scheme for the lattice 
gauge theory Hamiltonian in the magnetic basis, where the gauge links are unitary and diagonal. The digitization is obtained from a particular partitioning of the group manifold, with the canonical momenta constructed by an approximation of the Lie derivatives on this partitioning. This construction, analogous to a discrete Fourier transform, preserves the spectrum of the electric part of the Hamiltonian and the canonical commutation relations exactly on a subspace of the truncated Hilbert space, while the residual subspace can be projected above the cutoff of the theory.
© The Author(s) 2024
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