Questions tagged [quantum-field-theory]
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.
373
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2
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What does it mean to take the diagonal of the group $SU(2) \times SU(2) $?
I am reading Witten's paper on topological field theories, in specific the topological twist in page 359. In order to perform the twist he takes the diagonal subgroup of $K = SU(2)_{\text{Right}} \...
6
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0
answers
886
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Understanding Segal's definition of conformal field theory
I have a fundamental problem in understanding Segal's definition of a conformal field theory:
On the one hand his monoidal CFT-functor is a formalization of the fact that, physically, the integrand ...
1
vote
0
answers
94
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anomaly polynomial of generalized Hitchin system
I would like to ask about mathematical background of this object. So, I am trying to puzzle out with 4d $\mathcal{N}=2$ SQFT. As far as I can gather this theroy can be described in terms of ...
8
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0
answers
298
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Fock Space Proof of $(g(x)\phi^4)_2$ Mass Gap?
Is there a proof that does not depend on Euclidean methods? Is this a proof? :
$V(g)$ can be written as $P+R$ where $P$ is non-negative and $R$ is $N$-bounded (and hence $(H_0+\lambda P)$-bounded). $...
24
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6
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Quantum fields and infinite tensor products
As I understand it, a naive interpretation of the state space of a quantum field theory is an infinite tensor product
$$\otimes_{x\in M} H_x,$$
where $x$ runs over the points of space. This ...
22
votes
2
answers
8k
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How to learn QFT from mathematical perspective?
I want to learn QFT, because I have heard of its applications in mathematics, I am not interested in scattering cross sections and such. Where can I start to learn? Only books I found are either way ...
3
votes
1
answer
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Why is an extended T(Q)FT called fully local?
Hopefully this question does not double another. If so, don't bother to close this.
An extended topological quantum field theory is sometimes called, 'fully local".
Why is that? I can imagine that ...
9
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3
answers
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Reference for Hopf algebra applications to Feynman diagrams
I need to give a talk about Hopf algebras and I would like to give a (at least) 5 minutes introduction using Feynman diagrams as a motivation. I'm looking for a not-so-heavy reference explaining how ...
5
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1
answer
662
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AKSZ sigma models for higher spin
The AKSZ framework constructs 2D sigma models in the BV formalism. Is there a generalization of the AKSZ approach to higher spin?
10
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1
answer
982
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TQFT characterization of braiding statistics
In the TQFT language, quasiparticles correspond to Wilson loop operators. It is well-known that quasiparticles can have non-trivial braiding statistics.
Take $2+1$ dimensional Abelian Chern-Simons ...
1
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0
answers
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Dixon's diagram for BRS cohomology
The article by J. A. Dixon titled Calculation of BRS cohomology with spectral sequences (Comm. Math. Phys. Volume 139, Number 3 (1991), pages 495-526) describes in words a diagram that is not printed. ...
2
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2
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665
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Quantum Field theory - integral notation
I have a problem with understanding how the resolution of the identity of an operator is presented in some literature for physicists.
I'm a student of mathematics, and I understand the notion of a ...
4
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1
answer
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reference for higher spin - not gravitational nor stringy
Other than the papers of Berends, Burgers and van Dam, are there any papers that study the general case of deforming a free field theory with higher spin fields to be interactive?
1
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0
answers
242
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Fourier transform of a matrix represented compact lie group
In physics, I come across this kind of integration (in the nonlinear sigma model):
\begin{equation}
S[g] = \frac{1}{\lambda} \int d^dr\ \text{tr}[\triangledown g\triangledown g^{-1}]
\end{equation}
...
12
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0
answers
330
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Does the $(\mathbb Z/2)$-graded isomorphism $E_n \cong E_{n+2}$ have any nice properties?
This question assumes everything is dg. Let's decide to work over the "field" $\mathbb Q[\mu,\mu^{-1}]$ where $\mu$ has homological degree $+2$. Then chain complexes are just $\mathbb Z/2$-graded. ...
9
votes
2
answers
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What is the BRST-anti-BRST formalism?
What is the BRST-anti-BRST formalism?
Is the Sp(2) doublet the ghost, antighost pair?
Introductory accounts of this subject seem to be hard to find. I would appreciate a reference for someone who ...
16
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0
answers
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"extended TQFT" versus "TQFT with defects"
There are two ways in which higher categories appear in topological field theory: in extended TFTs and in TFTs with defects. How are these appearances related?
According to the Atiyah-Segal axioms, a ...
2
votes
0
answers
417
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Commutation relations for Dirac and Pauli electron
I hope this question makes sense.
Let $\phi$ be a quantized Dirac spinor with four components $\phi_{\alpha}$, $\alpha=1,2,3,4$. If we denote by $\pi$ the conjugate momentum, then they obey the ...
10
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5
answers
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Reference request for a treatment of Schwinger–Dyson equations
Is there a treatment of Schwinger–Dyson equations with no mention of Green's functions? Is there perhaps a purely algebraic analog?
6
votes
0
answers
279
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How to take this Grassmann integral?
I'm trying to reconstruct and understand what is explained in a paragraph of this paper. I am trying to check if the method they describe actually gives us the Laughlin state. The integral I'm facing ...
2
votes
0
answers
208
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Level quantization of 7d $SO(N)$ Chern-Simons action
In 3d, one can write down the $SO(N)$ Chern-Simons action to be $$S(A)=\frac{k}{192\pi}\int_{M}\text{Tr}(A d A +\frac{2}{3}A^3),$$ where $A$ is an $SO(N)$ connection. The level quantization can be ...
18
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2
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931
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Infinite dimensional 2-Hilbert spaces
Is there a definition of an infinite dimensional 2-Hilbert space?
Finite dimensional 2-Hilbert spaces have been discussed by Baez in
http://arxiv.org/abs/q-alg/9609018
In the more recent paper by ...
2
votes
0
answers
478
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Feynman integrals in algebraic geometry [closed]
In quantum field theory, multi-loop Feynman integrals are basic ingredients of calculating high order corrections. Recently, I have come across the paper A Feynman integral via higher normal functions....
1
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0
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106
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differential forms in double field theory
In double field theory, there are 'double differential forms' meaning that the standard 1-forms $d x^i$ generate an algebra over functions depending on both of the double coordinates
$x^i$ and $\tilde ...
6
votes
3
answers
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Some explanation about Dynin's formalism
I have seen this claim on the Wikipedia page for the Yang-Mills Millenium problem by Alexander Dynin. He is a mathematician working at the Department of Mathematics of Ohio State University and so, I ...
3
votes
1
answer
876
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Comparison of Different Types of QFT
As far as I can tell, there are a number of major types of quantum field theory. For example,
Constructive QFT, which has two major branches (Algebraic/Axiomatic QFT and Functorial QFT).
Topological ...
15
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2
answers
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4d Constructive Quantum Field Theory
As a follow up to my previous question (How does Constructive Quantum Field Theory work?), I was wondering what difficulties physicists have had constructing 4d axiomatic qfts. Why has CQFT's success ...
22
votes
2
answers
4k
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2d Ising model in conformal fields theory and statistical mechanics
I am not completely sure that this question is appropriate for this mathematical site. But since in the past I did get on MO couple of times nice answers to rather physical questions, I will try. ...
24
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0
answers
1k
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p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)
I am going to ask a question, at the end below, on whether anyone has tried to make more explicit what should be, it seems to me, a close relation between p-adic string theory and the refinement of ...
7
votes
0
answers
1k
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What is geometric engineering in quantum field theory?
Could someone help me to understand what geometric engineering in quantum field theory is? I didn't find any introductary articles online. Thank you!
Edit : Here is my background. I am math major. I ...
22
votes
1
answer
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Classical and Quantum Chern-Simons Theory
Please excuse a sloppy question from an old user who hasn't been here in a long time. I think the expertise here is such that it can be answered anyway.
Let $\Sigma$ be a two-manifold and $M$ a ...
4
votes
2
answers
2k
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Large vs Small Gauge transformations and Physical theories
I can't decipher the difference between large and small gauge transformations especially in its applications in physics.If perhaps one can engineer a simple physical theory that has such a ...
8
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3
answers
1k
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References request: constructive quantum field theory
I am taking a course this semester on QFT, which deals much with constructive quantum field theory. Some of its topics so far involve relationships between non-Gaussian probability measures,Feynman ...
2
votes
2
answers
825
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Quantization by cohomology
Ok, so I have heard some cool stuff here and there about how to Quantize Yang-Mills via cohomology, can anyone refer any texts in the literature that have shed some light on this, I mean I have some ...
9
votes
1
answer
679
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Duality between orbifold and quasi-Hopf algebra (twisted quantum doubles)
A quick Question:
Is there some duality known between the quasi Hopf algebra
$D^\omega(H)$ of a finite group $H$ to an orbifold model (such as
SU(2)/$G$ or SO(3)/$G$ orbifold of some group $G$)? What ...
3
votes
1
answer
576
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Some identities with the Riemann-Hurwitz zeta function
The only definition that I have ever seen of this Riemann-Hurtwitz zeta-function is this,
For $0 < a \leq 1$ we have the identity
$$ \zeta(z, a) = \frac{2 \Gamma(1 - z)}{(2 \pi)^{1-z}} \left[\sin ...
1
vote
1
answer
350
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zeta-function regularized integrals
I gather that the following two identities about $\xi(3)$ hold via some notion of zeta-function regularized integrals.
$\xi(3) = \frac{(2\pi)^3}{3}\int _0 ^\infty d\lambda \frac{\sqrt{\lambda} }{1 + ...
6
votes
1
answer
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Understanding the intermediate field method for the $\phi^4$ interaction
In Rivasseau's and Wang's How to Resum Feynman Graphs, on page 11 they illustrate the intermediate field method for the $\phi^4$ interaction and represent Feynman graphs as ribbon graphs. I had to ...
6
votes
0
answers
444
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Lagrangian (classical) BRST cohomology groups
I'm trying to understand BRST complex in its Lagrangian incarnation i.e. in the form mostly closed to original Faddeev-Popov formulation. It looks like the most important part of that construction (...
3
votes
1
answer
1k
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What are Euler density and Weyl invariants?
I would like to know as to what is the definition and significance of what are called "Euler density" and "Weyl invariants" (of weight $-d$ on a $d-$manifold)
Do many (which?) of them vanish when ...
3
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0
answers
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A gentle introduction to CFT [closed]
1) Which is the definition of a conformal field theory?
2) Which are the physical prerequisites one would need to start studying conformal field theories?
(i.e Does one need to know supersymmetry? ...
3
votes
1
answer
479
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The Fuchsian monodromy problem
I want to understand the argument being made from equation 6.1 to 6.5 in this paper between pages 27-28
6.2, 6.4 and 6.5 are completely out-of-the-blue to me and I have no clue as to from where they ...
8
votes
1
answer
514
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Are there exactly solvable CFTs?
I am wondering if there are CFTs such that n-point correlation functions in them of the fields (may be the primaries or of some notion of twist fields) is exactly known.
Are there such?
Aren't ...
4
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0
answers
298
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Proving conformal invariance of a field theory by property of its stress energy tensor.
I have a question about proving conformal invariance of a field theory by property of its stress energy tensor.
In physics there is argument that when the stress-energy tensor is traceless, symmetry,...
8
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1
answer
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What is the "Tangle" at the Heart of Quantum Simulation?
The following questions generalize and naturalize the question that was originally asked. Provisional answers largely due to Will Sawin are now included.
As was discussed in the question originally ...
20
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1
answer
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Gauss linking integral and quadratic reciprocity
In the setting of Mazur's "primes and knots" analogy, prime ideals $\mathfrak p\subset\mathcal O_K$ correspond to "knots" $\operatorname{Spec}\mathcal O_K/\mathfrak p$ inside a "3-manifold" $\...
72
votes
2
answers
9k
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The amplituhedron minus the physics
Is it possible to appreciate the geometric/polytopal properties of the amplituhedron without delving into the physics that gave rise to it?
All the descriptions I've so far encountered assume ...
2
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0
answers
102
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What are the boundary asymptotics of harmonic symmetric transverse traceless rank-s tensors on $\mathbb{H}^n$ in the Poincare upper-half-space model? [closed]
This question is motivated by the results in this paper, http://calvino.polito.it/~camporesi/JMP94.pdf
In this paper some of its most important results about the asymptotics of symmetric traceless ...
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2
answers
1k
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Regarding understanding differential geometry [closed]
I am essentially looking for a book that would hold my hand through basic concepts to more complicated ones. I am coming from physics. I am looking to make some connections with Classical mechanics ...
5
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1
answer
596
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Proof of the general expression for anomaly in a CFT and its partition function
I think the statement is that for any dimensional CFT the following is true,
$$\langle T^{\mu}_\mu \rangle = \sum B_n I_n - 2(-1)^{d/2}AE_d,$$
where $E_d$ is the `"Euler density" and $I_n$ are the ...