Speaker: Dr. Robert Oeckl
Title: States on timelike hypersurfaces
Abstract: A step towards general covariance in quantum field theory? The notion of state space in quantum theory is usually associated with hypersurfaces of space-time that need to be spacelike. Evolution in time plays then a distinctive role, essentially preventing a manifestly 4-covariant perspective on quantization from first principles. This restriction seems to have been rarely questioned, partly for good and partly for bad reasons, as we shall argue. We demonstrate that a generalized "general boundary" formalism makes sense, where states are associated to more general hypersurfaces and "evolution" is no longer necessarily a time-evolution. To this end we construct state spaces on certain time-like hypersurfaces in Klein-Gordon quantum field theory and evaluate associated transition amplitudes. We show that the physically correct scattering amplitudes emerge. A benefit of this formulation is that the usual crossing symmetry of transition amplitudes is not a "mysterious" emerging feature, but manifest in the formalism from the beginning. We also put particular emphasis on the discussion of the probability interpretation and the meaning of unitarity.
Talk: Transparencies, Recorded Talk