organized by the University of Potsdam and the Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
2th – 13th March 2015
The University of Potsdam and the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) offer a crash course on General Relativity and its astrophysical applications. This course can be attended by European students studying in their 5th semester Physics or Mathematics. The seminar consists of 3 lectures (to be held in English):
- Introduction to General Relativity (Oliver Rinne, Piotr Bizoń)
- Introduction to Higher-Spin Field Theories (Massimo Taronna)
- Modern approaches to scattering amplitudes (Oliver Schlotterer)
The timetable is arranged to provide two lectures in the morning, each one lasting 90 minutes. In the afternoon there will be opportunities for questions and discussions.
The lectures will take place daily from 9.00-10.30 and 11.00-12.30 in the lecture hall of the main building of the Max Planck campus in Golm (near Potsdam).
Address
Max Planck Institute for Gravitational Physics
Am Mühlenberg 1
14476 Potsdam-Golm
Contact
Abstracts
Introduction to General Relativity (Oliver Rinne, Piotr Bizoń)
We start with a review of special relativity from a geometrical point of view. Then we cover the mathematical material needed to understand general relativity, ending with the formulation of Einstein’s equations. Next, we give a brief introduction to gravitational radiation, one of the most important predictions of general relativity. Finally, we derive two important solutions of Einstein’s equations and discuss their properties: (i) the Schwarzschild metric (planetary motion, bending of light, black hole) and (ii) the Friedman-Robertson-Walker metrics (cosmological redshift, big bang, horizons)
Introduction to Higher-Spin Field Theories (Massimo Taronna)
The aim of these lectures is to provide a pedagogical introduction to higher-spin gauge theories. I will start with a quick review of the concept of spin and associated unitary representations on constant curvature backgrounds. I will then describe Fronsdal wave operators for higher-spin fields and corresponding free theories. We shall than move to the problem of introducing interactions focusing on the differences between higher-spin fields and their lower spin counterparts. Some emphasis will be put on various classical no-go results and to their assumptions and loopholes arriving to introduce Vasiliev’s equations and the mathematical tools needed to understand them.
Modern approaches to scattering amplitudes (Oliver Schlotterer)
These lectures cover modern techniques to compute scattering amplitudes in gauge theories and perturbative gravity. The textbook method of summing Feynman diagrams gives rise to unwieldy expressions which obscure their hidden simplicity and motivate alternative approaches. For this purpose, an organization scheme will be introduced to identify symmetries between color and kinematic degrees of freedom in gauge theory amplitudes and to express gravity amplitudes as their double copies. Moreover, elements of the pure spinor formalism will be introduced to compactly represent the elementary building blocks of gauge theory amplitudes with manifest supersymmetry. As a key virtue of pure spinor superspace, it allows to efficiently determine amplitudes from the underlying BRST symmetry.
Downloadable Files
- GR problems 1
- GR summary 1
- Exercises
- Lecture notes: Modern approaches to scattering amplitudes (ZIP-File, 19 MB)
Prerequisits
A working knowledge of freshman physics (classical mechanics, electromagnetism), and mathematics (advanced calculus, linear algebra) will be assumed. Some prior exposure to differential geometry is desirable but not required.
Complementary Reading
- S. Carroll, Spacetime and Geometry: An Introduction to General Relativity
- R.M. Wald, General Relativity (Part I)
- J. Stewart, Advanced General Relativity
- B.F. Schutz, A First Course in General Relativity
- J. Hartle, Gravity: An Introduction to Einstein’s General Relativity