Description
The main focus of this course is the exploration of the symmetry structure of General Relativity which is an essential step before any attempt at a (direct) quantization of GR. We will start by developing powerful tools for the analysis of local symmetries in physical theories (the covariant phase space method) and then apply it to increasingly complex theories: the parametrized particle, Yang--Mills theory, and finally General Relativity. We will discover in which ways these theories have similar symmetry structures and in which ways GR is special. We will conclude by reviewing classical results on the uniqueness of GR given its symmetry structure and discuss why it is so hard to quantize it. In tutorials and homeworks, through the reading of articles and collegial discussions in the classroom---as well as good old exercises---you will explore questions such as "Should general relativity be quantized at all? Is a single graviton detactable (even in principle)?", "What is the meaning of the wave functions of the universe?", "Can we do physics without time?".
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