Strict deformation quantization of abelian lattice gauge fields

This paper shows how to construct classical and quantum field C*-algebras modeling a $$U(1)^n$$ -gauge theory in any dimension using novel approach lattice gauge theory, while simultaneously constructing strict deformation quantization between the respective algebras. The construction starts with maps defined on operator systems (instead of C*-algebras) associated lattices, way that commutes all refinements, therefore giving rise map continuum (meaning ultraviolet infrared) limit. Although working at finite level, limit we obtain genuine C*-algebras. We also prove (classical quantum) are invariant under time evolutions related electric part abelian Yang–Mills. Our level essentially ones van Nuland Stienstra (Classical quantized resolvent algebras for cylinder, 2020. arXiv:2003.13492 [math-ph]), which admit completely general dynamics, briefly discuss ways extend this powerful result reduction, current setup should be generalized non-abelian case.