Schreiber
master thesis Nuiten

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about the cohomological quantization of local prequantum field theory in the context of differential cohomology in a cohesive topos. See also at Type-semantics for quantization.

This thesis won the GQT Student prize 2012-2013.

Contents

Abstract

We discuss how local prequantum field theories with boundaries can be described in terms n-fold correspondence diagrams in the (∞,1)-topos of smooth stacks equipped with higher circle bundles. This places us in a position where we can linearize the prequantum theory by mapping the higher circle groups into the groups of units of a ring spectrum, and then quantize the theory by a pull-push construction in the associated generalized cohomology theory.

We are particularly interested in the case of a 2d field theory, where the pull-push quantization takes values in the twisted K-theory of differentiable stacks. In such a way, we can produce quantum propagators along a cobordism and partition functions of boundary theories as maps between certain twisted cohomology spectra. Many quantization procedures found in the literature fit in this framework. For instance, propagators as maps between spectra have been considered in the context of string topology and in the realm of Chern-Simons theory, transgressed to two dimensions. Examples of partition functions of boundary theories are provided by the K-theoretic quantization of a Poisson manifold, seen as the boundary of its non-perturbative Poisson sigma model, together with the D-brane charges and “M-brane charges” that appear in string theory and M-theory.

Thesis presentation

The presentation talk is

  • Monday, August 26, 2013

    at 14.00,

    in BBL 071, Utrecht University.

Revised on September 11, 2014 21:39:22 by Yannick Voglaire? (158.64.77.102)