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For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.

11 votes
2 answers
610 views

What are the topological phases of quantum Hall systems?

(Fractional) quantum Hall systems are $2+1$-dimensional models which are said to possess topological order. One (maybe even complete) set of invariants of topological phases in $2+1$ dimensions is giv …
Andi Bauer's user avatar
  • 3,001
5 votes
0 answers
237 views

Does Dijkgraaf-Witten theory have a time-reversal symmetry?

The motivation why I'm asking is that in physics, models like Dijkgraaf-Witten are called "non-chiral" because they allow gapped boundaries, but on the other hand, people refer to models as "non-chiral …
Andi Bauer's user avatar
  • 3,001
11 votes
1 answer
667 views

Importance of the principal bundle in Chern-Simons theory

This is a very basic beginners question about Chern-Simons theory. The configurations that we sum over to get the partition function are given by a Lie-algebra valued 1-form $A$ on a topological 3-man …
Andi Bauer's user avatar
  • 3,001
21 votes
1 answer
1k views

Fully extended TQFT and lattice models

I often read that fully extended TQFTs are supposed to classify topological phases of matter. So I would like to understand the formal nature of fully extended TQFTs on a more direct physical level (w …
Andi Bauer's user avatar
  • 3,001