The Hamilton-Jacobi equation for a classical dynamical system naturally leads to an emergent notion of time in terms of the geometry of the configuration space. We illustrate this in a series of increasingly elaborate situations: particle mechanics on a fixed energy surface; non-Abelian gauge theories for compact semi-simple Lie groups where the Gauss law presents new features; and General Relativity in d > 2 where the metric on configuration space -- the de Witt metric -- has indefinite signature. We illustrate the formula for emergent time in General Relativity in various examples including de Sitter spacetime and asymptotically AdS spacetimes.
Zoom link: https://icts-res-in.zoom.us/j/88092766911?pwd=R3ZrVk9yeW96ZmQ4ZG9KRzVhenRKZz09
Meeting ID: 880 9276 6911
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