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12 votes
2 answers
1k views

Turaev-Viro extended TQFT

Hi I am looking for any papers which extends the Turaev-Viro TQFT to a 3-2-1 theory (i.e. allows manifolds with corners) . I know this construction is known, but I cannot find a source. Please help. ...
user1654's user avatar
  • 121
9 votes
2 answers
3k views

The Fock space vs the Hilbert space in the context of quantum field theory

Mathematically the definitions are as follows : if $H_n$ is a $n$-dimensional complex Hilbert space then its two different corresponding ``Fock space"(s) are often denoted as $F_{1}$ and $F_{-1}$ ...
gradstudent's user avatar
  • 2,246
7 votes
2 answers
654 views

What is the state in the WRT TQFT associated to a handlebody?

Let $Y^3$ be a handlebody with boundary $\Sigma$. By definition, there is some associated vector $v_{WRT}(Y^3)\in Z(\Sigma)$, the (finite dimensional) Hilbert space associated to $\Sigma$ by the ...
John Pardon's user avatar
  • 18.7k
5 votes
0 answers
114 views

Differential form TQFT for Walker-Wang model?

In terms of the TQFTs in continuous differential form gauge fields, what would the Walker-Wang lattice model describe? Obviously, there is a $BF$ theory part: $$\frac{N}{2 \pi}\int B dA$$ if it ...
miss-tery's user avatar
  • 755
1 vote
0 answers
79 views

Ordering in Cobordism Category

Let $Cob^{3}$ denote the cobordism category of $1$ dimensional manifolds i.e the objects are finite disjoint union of circles and morphisms are represented by surfaces. Is it possible to treat the ...
Monkey.D.Luffy's user avatar