Quantum Gravity (PW-10)10 ECTS
(englische Bezeichnung: Quantum Gravity)

Lehrveranstaltungen:

• • Quantum Gravity
    (Vorlesung, 4 SWS, Thomas Thiemann, Mi, 10:00 - 12:00, 14:00 - 16:00, HD; Einzeltermine am 10.5.2016, 14:00 - 16:00, 18:00 - 20:00, HF; 8.6.2016, 12:00 - 13:00, HD)
  • Tutorial for the Course Quantum Gravity
    (Tutorium, Thomas Thiemann et al., Fr, 16:00 - 19:00, SR 01.683, SR 01.779, SR 02.779, SR 02.729)

Inhalt:

Contents

1. Classical Preliminaries
1i. Einstein-Hilbert action, ADM formulation and Dirac’s constraint analysis
1ii. Observables, Problem of Time, Relational Formalism, Deparametrisation
1iii. Palatini and Holst action and initial value formulation
1iv. Connection formulation in 4D: Ashtekar-Barbero-Immirzi-Sen variables
1v. Connection formulation in any D: Hybrid connection

2. Hilbert space
2i. Yang-Mills like operators for QG: Magnetic holonomies and non-Abelian electric fluxes
2ii. Representation theory and states on the holonomy-flux star algebra
2iii. Diffeomorphism covariance, uniqueness theorem and Ashtekar-Isham-Lewandowski state
2iv. Properties of the Ashtekar-Isham-Lewandowski representation, gauge invariance and spin network basis
2v. Measure theory on the space of generalised connections and projective formulation

3. Geometric Operators
3i. Classical geometric volume of spatial, d-dimensional submanifolds
3ii. Length, area and volume functionals of curves, surfaces and regions in 4D
3iii. Quantisation and spectral properties of geometric operators in 4D: built in discreteness
3iv. Quantisation and spectral properties of geometric operators in higher D
3v. Quantum simplicity constraint operators in higher D

4. Dynamics
4i. Operator constraint approach I: Quantisation of spatial diffeomorphism constraint, distributional solutions and singular knot theory
4ii. Operator constraint approach II: Quantisation of Hamiltonian constraints, physical Hilbert space
4iii. Operator constraint approach III: Dirac algebra anomalies and Master constraint programme
4iv. Reduced phase space approach: Quantisation of the physical Hamiltonian for concrete deparametrising matter
4v. Quantisation of standard model and supersymmetric matter

5. Semiclassical Limit
5i. Complexifier coherent states
5ii. Semiclassical properties: Expectation values, saturation of Heisenberg uncertainty bound, annihilation operator eigenstates
5iii. Expectation value and fluctuation calculations for the physical Hamiltonian operator
5iv. Quantum field in Curved Space-time Limit
5v. Application to scattering theory on a fixed background geometry, gravitons, vacuum energy

6. Applications
6i. Path integral formulation: Spin foam models
6ii. Semiclassical Quantum Black holes and Hawking-Bekenstein Entropy counting
6iii. Symmetry reduced models: Quantum Cosmology
6iv. Quantum gravity phenomenology I: Possible modified dispersion relations and Gamma ray bursts
6v. Quantum Gravity phenomenology II: Possible QG imprints in the CMBR

Lernziele und Kompetenzen:

Learning goals and competences:
Students

• explain the relevant topics of the lecture

• apply the methods to specific examples

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:
Das Modul ist im Kontext der folgenden Studienfächer/Vertiefungsrichtungen verwendbar:

1. Physics (Master of Science)
   (Po-Vers. 2015s | NatFak | Physics (Master of Science) | Master examination | Master examination | Physics elective courses)
2. Physics (Master of Science)
   (Po-Vers. 2015s | NatFak | Physics (Master of Science) | Master examination | Master examination - Elite study program | Physics elective courses)
3. Physik (Bachelor of Science)
   (Po-Vers. 2010 | NatFak | Physik (Bachelor of Science) | Integrierter Bachelor- und Masterstudiengang (Forschungsstudiengang) | Module der Masterprüfung | Physics elective courses)

Studien-/Prüfungsleistungen:

Quantum Gravity (Prüfungsnummer: 503470)

(englischer Titel: Quantum Gravity)

Prüfungsleistung, mündliche Prüfung, Dauer (in Minuten): 45, benotet, 10 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

weitere Erläuterungen:
Freiwillige Zwischenprüfung: Die Bearbeitung von 50% der Hausaufgaben in sinnvoller Weise und die Präsentation von einer vollständig, überwiegend richtig gelösten Aufgabe während des Semesters führt zu einer Verbesserung um eine Notenstufe (0,3 oder 0,4 Notenpunkte).
Voluntary interim examination: Meaningful work on 50% of the homework problems and presentation of one complete, predominantly correct solution during the semester leads to an improved grade by 0.3 or 0.4.

Erstablegung: SS 2016, 1. Wdh.: SS 2016 (nur für Wiederholer)

1. Prüfer:

Thomas Thiemann