Spinors, Jets, and the Einstein Equations

Many important features of a eld theory, e.g., conserved currents, symplectic structures, energy-momentumtensors, etc., arise as tensors locally constructed from the elds and their derivatives. Such tensors are naturally de ned as geometric objects on the jet space of solutions to the eld equations. Modern results from the calculus on jet bundles can be combined with a powerful spinor parametrization of the jet space of Einstein metrics to unravel basic features of the Einstein equations. These techniques have been applied to computation of generalized symmetries and \characteristic cohomology" of the Einstein equations, and lead to results such as a proof of non-existence of \local observables" for vacuum spacetimes and a uniqueness theorem for the gravitational symplectic structure.