 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 spacetime that need to be spacelike. Evolution in time plays then a distinctive role, essentially preventing a manifestly 4covariant 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 timeevolution. To this end we construct state spaces on certain timelike hypersurfaces in KleinGordon 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

 