Groupoid Quantization of Loop Spaces

2012/03/27 by Christian Saemann, Richard J. Szabo, Saemann, Christian +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.1203.5921

openalex publication_date 2012/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review the various contexts in which quantized 2-plectic manifolds are expected to appear within closed string theory and M-theory. We then discuss how the quantization of a 2-plectic manifold can be reduced to ordinary quantization of its loop space, which is a symplectic manifold. We demonstrate how the latter can be quantized using groupoids. After reviewing the necessary background, we present the groupoid quantization of the loop space of R³ in some detail.

Cited by

• Nonassociative geometry and twist deformations in non-geometric string\n theory
• Extended Field Theories as higher Kaluza-Klein theories

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