1:30 pm MCP 201
On-Shell Covariance of Quantum Field Theory Amplitudes.
Scattering amplitudes in quantum field theory are independent of field parameterizations. They can be expressed in terms of geometric tensors in the (constant) field space manifold, which makes their covariance under non-derivative field redefinitions manifest. We generalize this geometric framework to the "manifold" of functional (configuration) space, which formally extends the amplitudes' manifest covariance to all allowed field redefinitions. On this "manifold", amplitudes satisfy a recursion relation that closely resembles the application of covariant derivatives to increase the rank of a tensor. This allows us to argue that (tree-level) amplitudes possess a notion of on-shell covariance, in that they transform as a tensor under any allowed field redefinition up to a set of terms that vanish when the equations of motion and on-shell momentum constraints are imposed.