  We suggest that in the proper definition, Quantum Field Theories are quantum
mechanical system which 'live' on the space of causal structures ${\cal C}$ of
spacetime. That is, for any QFT a Hilbert space ${\cal H}$ on which local
operators live is assigned not for each Lorentzian metric $g$, but for each
causal structure ${\cal C}$. In practice one uses 'conformal frames' which all
provide equivalent descriptions of the same QFT. To put it differently, Quantum
Field Theories only know about causal structure of spacetime, and not its full
Lorentzian metric. The Weyl group and the local RG flow naturally arise when
one compares equivalent descriptions in different conformal frames. This is
reduced to the usual RG flow of coupling constants when one only compares
descriptions in conformal frames related by spacetime-independent Weyl
rescalings. We point out that in this picture minimal coupling of a QFT to the
metric is inconsistent and comment on the necessary violation of the
equivalence principle in the presence of scalars.
