Groupoid Quantization of Loop Spaces

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 R^3 in some detail.

19 pages, Proceedings of the Corfu Summer Institute 2011 - School and Workshops on Elementary Particle Physics and Gravity, September 4-18, 2011, Corfu, Greece

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Cited by in corpus (5)

• Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry
• Twisted Poisson Structures and Non-commutative/non-associative Closed String Geometry
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• Automorphisms of Strong Homotopy Lie Algebras of Local Observables
• Extended Field Theories as higher Kaluza-Klein theories