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1. Nuiten, J.J. Cohomological quantization of local prequantum boundary field theory.

Degree: 2013, Universiteit Utrecht

URL: http://dspace.library.uu.nl:8080/handle/1874/282756

We discuss how local prequantum field theories with boundaries can be described in terms of n-fold correspondence diagrams in the infinity-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. In such a way, we can produce quantum propagators along cobordisms and partition functions of boundary theories as maps between certain twisted cohomology spectra. We are particularly interested in the case of 2d boundary field theories, where the pull-push quantization takes values in the twisted K-theory of differentiable stacks.
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 partitions functions of boundary theories are provided by the D-brane charges appearing in string theory and the K-theoretic quantization of symplectic manifolds. Here we extend the latter example to produce a K-theoretic quantization of Poisson manifolds, viewed as boundaries of the non-perturbative Poisson sigma-model. This involves geometric quantization of symplectic groupoids as well as the K-theoretic formulation of Kirillovâ€™s orbit method. At the end we give an outlook on the 2d string sigma-model on the boundary of the membrane, quantized over tmf-cohomology with partition function the Witten genus.
*Advisors/Committee Members: Henriques, dr. A.G..*

Subjects/Keywords: quantum field theory; quantization; generalized cohomology; K-theory

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Nuiten, J. J. (2013). Cohomological quantization of local prequantum boundary field theory. (Masters Thesis). Universiteit Utrecht. Retrieved from http://dspace.library.uu.nl:8080/handle/1874/282756

Chicago Manual of Style (16^{th} Edition):

Nuiten, J J. “Cohomological quantization of local prequantum boundary field theory.” 2013. Masters Thesis, Universiteit Utrecht. Accessed September 24, 2020. http://dspace.library.uu.nl:8080/handle/1874/282756.

MLA Handbook (7^{th} Edition):

Nuiten, J J. “Cohomological quantization of local prequantum boundary field theory.” 2013. Web. 24 Sep 2020.

Vancouver:

Nuiten JJ. Cohomological quantization of local prequantum boundary field theory. [Internet] [Masters thesis]. Universiteit Utrecht; 2013. [cited 2020 Sep 24]. Available from: http://dspace.library.uu.nl:8080/handle/1874/282756.

Council of Science Editors:

Nuiten JJ. Cohomological quantization of local prequantum boundary field theory. [Masters Thesis]. Universiteit Utrecht; 2013. Available from: http://dspace.library.uu.nl:8080/handle/1874/282756

Universiteit Utrecht

2. Maes, J. An Introduction to the Orbit Method.

Degree: 2011, Universiteit Utrecht

URL: http://dspace.library.uu.nl:8080/handle/1874/205802

The Orbit Method is a method to determine all irreducible unitary representations
of a Lie group. It is entangled with its physical counterpart geometric
quantization, which is an extension of the canonical quantization scheme to
general curved manifolds. The main ingredient of the Orbit Method is the
notion of coadjoint orbits, which will be explained. Coadjoint orbits of a Lie
group have the natural structure of a symplectic manifold, as does the phase
space of a classical mechanical system. Naturally, geometric quantization
will be treated next, since it attempts to provide a geometric interpretation
of quantization within an extension of the mathematical framework of classical
mechanics (symplectic geometry). In particular, the axioms imposed on
a quantization will be discussed. Finally, as an application, coadjoint orbits
and geometric quantization will be brought together by indicating how to
determine the irreducible unitary representations of SU(2) by means of the
Orbit Method.
*Advisors/Committee Members: Henriques, Dr. A.G..*

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Maes, J. (2011). An Introduction to the Orbit Method. (Masters Thesis). Universiteit Utrecht. Retrieved from http://dspace.library.uu.nl:8080/handle/1874/205802

Chicago Manual of Style (16^{th} Edition):

Maes, J. “An Introduction to the Orbit Method.” 2011. Masters Thesis, Universiteit Utrecht. Accessed September 24, 2020. http://dspace.library.uu.nl:8080/handle/1874/205802.

MLA Handbook (7^{th} Edition):

Maes, J. “An Introduction to the Orbit Method.” 2011. Web. 24 Sep 2020.

Vancouver:

Maes J. An Introduction to the Orbit Method. [Internet] [Masters thesis]. Universiteit Utrecht; 2011. [cited 2020 Sep 24]. Available from: http://dspace.library.uu.nl:8080/handle/1874/205802.

Council of Science Editors:

Maes J. An Introduction to the Orbit Method. [Masters Thesis]. Universiteit Utrecht; 2011. Available from: http://dspace.library.uu.nl:8080/handle/1874/205802