Wave equations on Lorentzian manifolds and Quantization

Wave equations on Lorentzian manifolds and Quantization

Semester
SoSe 2022

Lecturer
Bernd Ammann

Type of course (Veranstaltungsart)
Seminar

German title
Wellengleichungen auf lorentzschen Mannigfaltigkeiten und Quantisierung

Contents
The main concern of the seminar is to solve geometrically motivated hyperbolic partial differential equations on curved backgrounds. The simplest example is the wave equation on (flat) $\mR^n$ whose solution will be the starting point of the seminar. These solutions can be used to iteratively construct solutions on curved spacetimes, i.e. Lorentzian manifolds. As soon as we have solved these equations, we will construct natural $C^*$-algebras to a given space-time which is a key step in the quantization of fields in physics, although the seminar is purely of a mathematical nature. We follow a book by Bär, Ginoux and Pfäffle which is self-contained to a very large degree and didactically very efficient. More information may be found in the program of the seminar which is available on the web page of the seminar, linked below.

Literature

C. Bär, N. Ginoux, F. Pfäffle. Wave Equations on Lorentzian Manifolds and Quantization, ESI Lectures in Mathematics and Physics, EMS. Available as E-Book in our library.
From a UR computer or via VPN the book can be downloaded at https://doi.org/10.4171/037.
Further literature is given in the program of the seminar, see below.

Recommended previous knowledge
The seminar addresses, in particular, to students who have followed my lecture about differential geometry II in the summer term 2021. Students with knowledge of differential geometry I might follow as well, if they are willing to read a bit of additional literature.
Necessary

Good knowledge about differential geometry as e.g. taught in "Differential geometry I".
Some basic knowledge about Lorentzian manifolds or willingness to read into this.

Helpful (can also be learnt within the seminar)

Improved understanding of Lorentzian manifold, e.g. de (Anti-) deSitter space
Basic knowledge about hyperbolic partial differential equations
Basic knowledge about C^*-algebras
Basic knowledge about quantization

Time/Date
Thursday 14-16

Location
M009

Course homepage
https://ammann.app.uni-regensburg.de/lehre/2022s_wave-equations
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Organisational meeting/distribution of topics: Monday, Feb 7th, 16.15 in M009, see website for
zoom access
If you want to participate, you are encouraged to send an email to me as soon as possible
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Presentation: Giving a seminar talk of roughly 90 minutes

Examination (Prüfungsleistungen)

Detailed written report of the seminar talk

Additional comments
Please register on GRIPS as we will distribute information via GRIPS

Modules
BV, BSem, MV, MSem, LA-GySem

ECTS
BSem und MSem: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16. LA-GySem:
6 LP. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16
+++ weitere Details: siehe Modulkatalog +++