Tobias Diez

Tobias Diez
Delft University of Technology | TU · Department of Applied Mathematics

Dr.

About

17
Publications
1,698
Reads
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41
Citations
Citations since 2016
14 Research Items
38 Citations
20162017201820192020202120220246810
20162017201820192020202120220246810
20162017201820192020202120220246810
20162017201820192020202120220246810
Introduction
My research is motivated by conceptual and mathematical problems of classical field theory, which I try to attack within the framework of infinite-dimensional differential geometry. In particular, I am interested in infinite-dimensional Hamiltonian systems and their reduced phase spaces (in particular, with applications towards gauge theory).
Additional affiliations
January 2015 - June 2015
École Polytechnique Fédérale de Lausanne
Position
  • Visiting student
August 2014 - February 2019
October 2013 - April 2014
Université de Lille
Position
  • Visiting student

Publications

Publications (17)
Preprint
Full-text available
We develop a powerful framework to calculate expectation values of polynomials and moments on compact Lie groups based on elementary representation-theoretic arguments and an integration by parts formula. In the setting of lattice gauge theory, we generalize expectation value formulas for products of Wilson loops by Chatterjee and Jafarov to arbitr...
Article
Full-text available
Local normal form theorems for smooth equivariant maps between infinite-dimensional manifolds are established. These normal form results are new even in finite dimensions. The proof is inspired by the Lyapunov–Schmidt reduction for dynamical systems and by the Kuranishi method for moduli spaces. It uses a slice theorem for Fréchet manifolds as the...
Preprint
Full-text available
Using a nonlinear version of the tautological bundle over Graßmannians, we construct a transgression map for differential characters from $M$ to the nonlinear Graßmannians $\mathrm{Gr}^S(M)$ of submanifolds of $M$ of a fixed type $S$. In particular, we obtain prequantum circle bundles of the nonlinear Graßmannian endowed with the Marsden-Weinstein...
Article
Full-text available
We prove a theorem on singular symplectic cotangent bundle reduction in the Fréchet setting and apply it to Yang–Mills–Higgs theory with special emphasis on the Higgs sector of the Glashow–Weinberg–Salam model. For the latter model, we give a detailed description of the reduced phase space and show that the singular structure is encoded in a finite...
Article
Full-text available
Let $M$ be a manifold with a closed, integral $(k+1)$-form $\omega $, and let $G$ be a Fréchet–Lie group acting on $(M,\omega )$. As a generalization of the Kostant–Souriau extension for symplectic manifolds, we consider a canonical class of central extensions of ${\mathfrak{g}}$ by ${\mathbb{R}}$, indexed by $H^{k-1}(M,{\mathbb{R}})^*$. We show th...
Article
Full-text available
The space of smooth sections of a symplectic fiber bundle carries a natural symplectic structure. We provide a general framework to determine the momentum map for the action of the group of bundle automorphism on this space. Since, in general, this action does not admit a classical momentum map, we introduce the more general class of group-valued m...
Conference Paper
Full-text available
Given a closed surface endowed with a volume form, we equip the space of compatible Riemannian structures with the structure of an infinite-dimensional symplectic manifold. We show that the natural action of the group of volume-preserving diffeomorphisms by push-forward has a group-valued momentum map that assigns to a Riemannian metric the canonic...
Article
Full-text available
Inspired by the Clebsch optimal control problem, we introduce a new variational principle that is suitable for capturing the geometry of relativistic field theories with constraints related to a gauge symmetry. Its special feature is that the Lagrange multipliers couple to the configuration variables via the symmetry group action. The resulting con...
Thesis
Full-text available
A local normal form theorem for smooth equivariant maps between Fr\'echet manifolds is established. Moreover, an elliptic version of this theorem is obtained. The proof these normal form results is inspired by the Lyapunov-Schmidt reduction for dynamical systems and by the Kuranishi method for moduli spaces, and uses a slice theorem for Fr\'echet m...
Preprint
Full-text available
Let $M$ be a manifold with a closed, integral $(k+1)$-form $\omega$, and let $G$ be a Fr\'echet-Lie group acting on $(M,\omega)$. As a generalization of the Kostant-Souriau extension for symplectic manifolds, we consider a canonical class of central extensions of $\mathfrak{g}$ by $\mathbb{R}$, indexed by $H^{k-1}(M,\mathbb{R})^*$. We show that the...
Conference Paper
Full-text available
JabRef is a reference management system mostly used by LaTeX users to organize their bibliographic references. As it is often the case in free and open source software, the usability of this program has not yet been analyzed systematically. In this paper, we report on the first application of user-centered design methods in this project. To identif...
Preprint
Full-text available
We prove a theorem on singular symplectic cotangent bundle reduction in the Fréchet setting and apply it to Yang-Mills-Higgs theory with special emphasis on the Higgs sector of the Glashow-Weinberg-Salam model. For the latter model we give a detailed description of the reduced phase space and show that the singular structure is encoded in a finite-...
Article
Full-text available
We establish a general slice theorem for the action of a locally convex Lie group on a locally convex manifold, which generalizes the classical slice theorem of Palais to infinite dimensions. We discuss two important settings under which the assumptions of this theorem are fulfilled. First, using Glöckner's inverse function theorem, we show that th...
Article
Full-text available
Given a principal bundle on an orientable closed surface with compact connected structure group, we endow the space of based gauge equivalence classes of smooth connections relative to smooth based gauge transformations with the structure of a Fréchet manifold. Using Wilson loop holonomies and a certain characteristic class determined by the topolo...
Thesis
Full-text available
A general slice theorem for the action of a Fréchet Lie group on a Fréchet manifolds is established. The Nash-Moser theorem provides the fundamental tool to generalize the result of Palais to this infinite-dimensional setting. The presented slice theorem is illustrated by its application to gauge theories: the action of the gauge transformation gro...
Article
Metal-semiconductor field-effect transistors (MESFET) are commonly known from GaAs technology [1] and are widely used for high-speed logic circuits due to their high channel mobility [2,3]. In contrast to GaAs-MESFET, which consist of an n-type implanted channel in a p-type or semi-insulating GaAs substrate, oxide MESFET consist of a thin semicondu...
Article
The stability of the figures of merit of transparent inverter circuits at temperatures up to 150°C and under illumination by light in the visible spectral range is investigated. The inverter circuits consist of two transparent metal-semiconductor field-effect transistors. For temperatures up to 150°C, the inverters remain operational; the gate elec...

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