Develop continuum versions of ultracold-atom lattice gauge models for direct comparison with continuum PQED/PGQED predictions

Develop continuum (a_L → 0) field-theoretic versions of ultracold-atom lattice gauge models proposed to simulate U(1) gauge dynamics in (2+1) dimensions, enabling direct comparison of tunable interaction strengths and nonperturbative phenomena with continuum predictions of Pseudo QED (PQED) and Pseudo Generalized QED (PGQED).

Background

The authors discuss quantum simulation proposals with ultracold atoms for realizing QED-like physics in two spatial dimensions and highlight the importance of comparing such lattice implementations to continuum field-theory predictions. They note that continuum limits (taking the lattice spacing a_L → 0) would facilitate parameter matching and theoretical–experimental consistency.

However, according to the authors, continuum versions of these lattice models are currently unknown. Constructing such continuum formulations—potentially aligned with PQED/PGQED’s pseudo-differential kernels—would bridge quantum simulation platforms and continuum theory, especially for strong-coupling regimes relevant to dynamical mass generation.