Examples of Riemannian Functorial Quantum Field Theory

Doctoral Dissertation

Abstract

Following Atiyah, Segal, Kontsevich and others, a $d$-dimensional Riemannian Functorial Quantum Field Theory $E$ assigns to a closed $d-1$ dimensional oriented Riemannian manifold a Hilbert space $E(Y)$ and to a bordism $Sigma$ from $Y1$ to $Y2$(which is a compact oriented Riemannian manifold with $partialSigma=Y2sqcup overline{Y1}$) a Hilbert-Schmidt operator $E(Sigma):E(Y1) o E(Y2)$ so that gluing bordisms corresponds to composing the associated operators. If we forget the Riemannian structure on the $Y$‘s and the bordisms, then there are many examples which are known has Topological Quantum Field Theories. In 2007, Douglas Pickrell constructed a family of examples of $2$-dimensional theory. In this dissertation, we construct examples of $d$-dimensional theory when $d$ is even.

Attributes

Attribute NameValues
URN
  • etd-07022014-135044

Author Santosh Kandel
Advisor Stephan Stolz
Contributor Brain Hall, Committee Member
Contributor Stephan Stolz, Committee Chair
Contributor Bruce Williams, Committee Member
Contributor Liviu Nicolaescu, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2014-05-28

Submission Date 2014-07-02
Country
  • United States of America

Subject
  • Fock spaces

  • Functorial Quantum Field Theory

  • Gaussian meaures

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility and Access Public
Embargo Release Date
  • 2015-07-10

Content License
  • All rights reserved

Departments and Units

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