Groupoid Quantization of Loop Spaces

Christian Saemann; Richard J. Szabo

Groupoid Quantization of Loop Spaces

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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.

Original language	English
Title of host publication	Proceedings of the Corfu Summer Institute 2011
Number of pages	19
Publication status	Published - 2012

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title = "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.",

author = "Christian Saemann and {J. Szabo}, Richard",

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

year = "2012",

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AU - Saemann, Christian

AU - J. Szabo, Richard

N1 - 19 pages, Proceedings of the Corfu Summer Institute 2011 - School and Workshops on Elementary Particle Physics and Gravity, September 4-18, 2011, Corfu, Greece

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

M3 - Conference contribution

BT - Proceedings of the Corfu Summer Institute 2011

ER -

Groupoid Quantization of Loop Spaces

Abstract

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