Quantum field theories in classical spacetimes and particles

According to a Received View, relativistic quantum field theories (RQFTs) do not admit particle interpretations. This view requires that particles be localizable and countable, and that these characteristics be given mathematical expression in the forms of local and unique total number operators. Various results (the Reeh-Schlieder theorem, the Unruh Effect, Haag's theorem) then indicate that formulations of RQFTs do not support such operators. These results, however, do not hold for non-relativistic QFTs. I argue that this is due to the absolute structure of the classical spacetimes associated with such theories. This suggests that the intuitions that underlie the Received View's choice of mathematical representations of localizability and countability are non-relativistic. Thus, to the extent that such intuitions are inappropriate in the relativistic context, they should be abandoned when it comes to interpreting RQFTs.

Research Hightlights► Absolute temporal metric is necessary for local and unique total number operators. ► Intuitions informing received view's representation of particles are non-relativistic. ► Particle interpretations of RQFTs may still be viable.