Representational Quantum Field Theory

A different approach to quantum field theory (QFT) in curved spacetime is proposed. In the conventional approach one often proceeds in the following way: one observer starts on a particular spacelike Cauchy hypersurface, defines there his positivefrequency mode functions, and integrates forward and back to find them everywhere. He thus ends up with a representation of that QFT. Another observer does likewise but starts on a different hypersurface. He ends up with a different representation of the QFT. In general, these two representations will not be unitarily equivalent. They will, of course, be related by a Bogoliubov transformation (BT corresponding to an operator B). Say the observers are interested in the value of some Hermitian operator O that describes an observable. The first finds. Using the BT the second observer re-expresses his operator in terms of the creation and annihilation operators of the first observer. He wants to find. Most critically, he assumes he can act with B O B-1 on his state and that it will produce the same result it would were he in the same state as the first observer. Essentially, he treats B |Y> as if it were |Y>. He may, therefore, find a different result. The assumption is that there is one common |Y> for both observers. It is this assumption we reject. The two observers have each defined their own Fock spaces and the operators of one can never act on the states of the other. Otherwise we are dealing with unitarily equivalent representations, which, in general, we are not. A common approach to dealing with this problem is Algebraic QFT in which Fock space drops from consideration. We will not be doing this, however. We propose something very different. And we give priority to the physical data. The observers must end up with the same result. We do not think there can ever be any disagreement about this. This change of protocol carries with it some interesting consequences. For one thing, the Parker effect goes away. But the Unruh effect and, perhaps, Hawking radiation survive largely unaltered.