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For questions about mathematical problems arising from quantum field theory, the branch of physics which describes subatomic particles and their interactions in terms of perturbations of the corresponding scalar, vector or tensor fields.

2 votes
0 answers
131 views

Rigorous QFT from integration over subspace

Many perturbative QFTs suffer from the lack of a rigorous definition of a "good enough" measure over the space of paths (or fields) $P$, $$\mathcal{Z} = \int_{{x \in P}} e^{iS(x)} Dx$$ There are many …
1 vote
2 answers
240 views

Link invariants from Hecke relations of higher order

Alexander theorem says oriented links in $\mathbb{R}^3$ can be represented by closures of braids. Markov theorem says that braids related by Markov moves produce isotopic braid closures, and vice vers …
25 votes
1 answer
2k views

Definition of an n-category

What's the standard definition, if any, of an $n$-category as of 2020? The literature I can tap into is quite limited, but I'll try my best to list what I had so far. In [Lei2001], Leinster demonstrat …
9 votes
0 answers
202 views

Donaldson invariants for piecewise-linear $4$-manifolds

It is well known that in dimension $4$, the notion of piecewise linear manifolds and the notion of smooth manifolds are the same [1][2]. On the other hand, the computations of Donaldson invariants inv …
7 votes
0 answers
220 views

Representations of 2-groups and quantum double constructions

Let $G$ be a finite group. The category of its representations (complex linear, finite dimensional, throughout this whole question) is equivalent to $\mathbb{C}[G]$-modules. V. Drinfeld constructed a …
12 votes
2 answers
1k views

A toy model in 0-d QFT

Questions For any positive integer $r$, compute $$(\frac{d}{dY})^r e^{(Y^2)}| _{Y=0}.$$ The answer should directly relates to a counting problem about Feynman diagrams. Is there a tutorial for how F …
5 votes
0 answers
126 views

Uniqueness of Witten-Dijkgraaf 2D TQFT at 0th dimension

If I understand correctly, Dijkgraaf-Witten TQFT in dimension 2 is the following. Fix any finite group $G$, we define a field over a closed 2-manifold to be a principle $G$ bundle (it's automatically …