# Most natural tensor structure for a quantum field

A quantum field is described by a Hilbert space. In many instances, the chosen tensor structure on this Hilbert space corresponds to that of space-like separated regions of space-time. The justification to this is that we can only perform local measurements, so the tensor structure should correspond to what subsystems operationally are, e.g. space-like separated regions of space-time. Does any one know a paper where the choice of a tensor structure for quantum fields is better motivated, and alternative tensor product structure proposed (for example in the context of relativistic quantum information, where space-like separated regions should not be the fundamental unit anymore since communication is generally allowed)?

• I think Wald talks about this a bit in chapter 12 of his GR book. – PPR Jun 15 '14 at 9:24