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Conformal Geometry, Tractors, and Physics

QMAP Seminar

Speaker: Abrar Shaukat, UC Davis
Location: 3240 MSB
Start time: Fri, Jan 18 2008, 3:10PM

The quotient SO(n+1,1)/P, where P is a parabolic subgroup, can be taken as the local model for conformal geometry on an n-manifold M. Using a Yang-Mills SO(n+1,1)-connection, we recover the "tractor connection", which lets us easily construct a conformally invariant Lagrangian, invariants of a conformal structure, and conformally invariant differential operators. We give concrete examples of such "tractor operators", and show how they arise naturally in the second quantized, ambient construction approach to conformal geometry. We also explain the physical meaning of tractor functions using first quantization.