Timo Jakobs: Canonical Momenta in Digitized SU(2) Lattice Gauge Theory: Definition and Free Theory

Monday 15 May 2023, 16:15 → 17:15 Europe/Berlin

Nußallee 14-16/3.013 (HISKP) - Seminar Room II (HISKP)

Speaker: Timo Jakobs (HISKP)

Title: 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 $\mathcal{H}$.  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 discretizing 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 ot  the Laplace-Beltrami operator on $S_3$ and show that the spectrum of  the free theory is reproduced again up to discretisation effects.