  While it has become widely appreciated that defining (higher) gauge theories
requires, in addition to ordinary phase space data, also "flux quantization"
laws in generalized differential cohomology, there has been little discussion
of the general rules, if any, for lifting Poisson-brackets of
(flux-)observables and their quantization from traditional phase spaces to the
resulting higher moduli stacks of flux-quantized gauge fields.
  In this short note, we present a systematic analysis of (i) the canonical
quantization of flux observables in Yang-Mills theory and (ii) of valid flux
quantization laws in abelian Yang-Mills, observing (iii) that the resulting
topological quantum observables form the homology Pontrjagin algebra of the
loop space of the moduli space of flux-quantized gauge fields.
  This is remarkable because the homology Ponrjagin algebra on loops of moduli
makes immediate sense in broad generality for higher and non-abelian
(non-linearly coupled) gauge fields, such as for the C-field in 11d
supergravity, where it recovers the quantum effects previously discussed in the
context of "Hypothesis H".
