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Results tagged with mp.mathematical-physics
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user 115363
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
2
votes
2
answers
206
views
Sum over exponentiated bilinear form in finite-field vector space
Let $A$ be a linear map over the finite-field vector space $(\mathbb F_2)^n$, i.e., an $\mathbb F_2$-valued $n\times n$ matrix, not necessarily symmetric. I'm interested in the sum
$$Z(A) = \sum_{X\i …
- 2,839
11
votes
1
answer
569
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 …
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4
votes
0
answers
179
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What is the value of the partition function of CFT on a compact conformal manifold?
Is the value of the partition function of a 2d CFT on a compact conformal manifold well defined? Or is there some kind of "anomaly" that makes it dependent on a bulk or some other kind of further stru …
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4
votes
Is a unitary Hamiltonian TQFT the same as a unitary axiomatic TQFT?
On the Hamiltonian level, the (axiomatic) TQFT tensors correspond to the imaginary time evolution of a microscopic system, not the real-time evolution (which would be a unitary operator). So there's n …
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7
votes
0
answers
234
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Why are Levin-Wen/Turaev-Viro models said to be non-chiral?
I'd like to bring together the following two notions of "non-chiral":
On the abstract algebraic side, a modular fusion category describing the anyon content of some physical system is said to be non- …
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7
votes
0
answers
131
views
What are the generators and relations of the conformal cobordism category?
According to a definition by Segal, a $2$-dimensional CFT is a symmetric monoidal functor from the category of oriented conformal cobordisms to the cateogry of projective complex vectorspaces. Coming …
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4
votes
0
answers
169
views
CFT as an axiomatic field theory
I'm trying to understand CFT from a purely axiomatic-field-theoretical perspective. That is, there is a vector space $V$ associated to the circle, and an element of $V^{\otimes n}$ associated to every …
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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 …
- 2,839
5
votes
0
answers
210
views
Does Dijkgraaf-Witten theory have a time-reversal symmetry?
By having a time-reversal symmetry I mean that there is a local anti-unitary symmetry (representing the non-trivial element of $Z_2$) of the state-sum construction (or, if you want, of the associated …
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11
votes
2
answers
382
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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 …
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