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In this article a new formulation of the Weyl C*-algebra, which has beeninvented by Fleischhack, in terms of C*-dynamical systems is presented. Thequantum configuration variables are given by the holonomies along paths in agraph. Functions depending on these quantum variables form the analyticholonomy C*-algebra. Each classical flux variable is quantised as an element ofa flux group associated to a certain surface set and a graph. The quantisedspatial diffeomorphisms are elements of the group of bisections of a finitegraph system. Then different actions of the flux group associated to surfacesand the group of bisections on the analytic holonomy C*-algebra are studied.The Weyl C*-algebra for surfaces is generated by unitary operators, whichimplements the group-valued quantum flux operators, and certain functionsdepending on holonomies along paths that satisfy canonical commutationrelations. Furthermore there is a unique pure state on the commutative WeylC*-algebra for surfaces, which is a path- or graph-diffeomorphism invariant.

AQV II. A new formulation of the Weyl C*-algebra