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Recently I was reading in Stephen B. Sontz' "Principal bundles - The quantum case" and in contrast to "the classical case" he offered almost no connections with physical concepts.

For quantum groups and algebras I know that there are links with modern TQFT constructions (such as in the work of Witten or Turaev-Viro). However for notions like Quantum Principal Bundles I could not find anything more than the papers of Durdevich (referenced by Sontz in his book) about the quantum versions of classical gauge theories.

Are there any other (well-)known applications of quantum principal bundles in the (mathematical-) physics literature or even in the mathematics literature?

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