Geometric Quantization Extended: A Path-Based Approach
Research Paper#Geometric Quantization, Quantum Mechanics, Mathematical Physics🔬 Research|Analyzed: Jan 3, 2026 16:40•
Published: Dec 31, 2025 05:02
•1 min read
•ArXivAnalysis
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.
Key Takeaways
- •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.
Reference / Citation
View Original"The paper identifies the obstruction to the existence of the Prequantum Groupoid as the non-additivity of the integration of the prequantum form on the space of loops."