Representations of the Weyl Algebra in Quantum Geometry
Representations of the Weyl Algebra in Quantum Geometry
The Weyl algebra $${\mathfrak{A}}$$ of continuous functions and exponentiated fluxes, introduced by Ashtekar, Lewandowski and others, in quantum geometry is studied. It is shown that, in the piecewise analytic category, every regular representation of $${\mathfrak{A}}$$ having a cyclic and diffeomorphism invariant vector, is already unitarily equivalent to the fundamental representation. …