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Results tagged with quantum-field-theory
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user 124549
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.
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 …
- 5,230
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 …
- 5,230
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 …
- 5,230
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 …
- 5,230
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 …
- 5,230
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 …
- 5,230
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 …
- 5,230