July 3, 2025
For any connected and simply connected parasymplectic space (X,ω) with group of periods Pω we construct a prequantum groupoid Tω as a diffeological quotient of the space of paths in X. This object serves as a unified structure for prequantization. The groupoid Tω has X as its objects, and its space of morphisms Y carries a canonical left-right invariant 1-form λ whose
curvature encodes ω. The isotropy group Tω,x at any point x , arising as a quotient of the space of loops, is isomorphic to the torus of periods Tω = R/Pω
