Geometric Quantization Extended: A Path-Based Approach

This paper extends the geometric quantization framework, a method for constructing quantum theories from classical ones, to a broader class of spaces. The core contribution lies in addressing the obstruction to quantization arising from loop integrals and constructing a prequantum groupoid. The authors propose that this groupoid itself represents the quantum system, offering a novel perspective on the relationship between classical and quantum mechanics. The work is significant for researchers in mathematical physics and related fields.

• •Extends geometric quantization to arbitrary connected parasymplectic diffeological spaces.
• •Introduces a Total Group of Periods to address quantization obstructions.
• •Proposes the Prequantum Groupoid as the Quantum System itself.
• •Establishes an isomorphism between the automorphisms of the Quantum System and the symmetries of the Dynamical System.