Questions tagged [non-perturbative]
Use this for questions which discuss models of quantum theories which do not make use of peturbation theory.
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What would a non-perturbative renormalization group treatment for polymers look like?
I know that one can do perturbative renormalization for the polymer excluded volume problem or the self-avoiding walk problem corresponding to n=0 component field theory. Here in Hamiltonian, we have, ...
2
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1answer
187 views
Why is lattice QCD called non-perturbative?
Like, if you are approximating a smooth structure with a discrete lattice, isn't this like a perturbation from smooth space-time?
If Feynman diagrams are a perturbative method, why are Feynamn ...
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32 views
How does Atiyah-Singer index theorem relates instanton number to number of fermion zero modes?
I was studying this paper, where the authors consider an $SU(2)$ gauge field of instanton number 1 on a 4-sphere $M =S^4$. If $n_L$ is the number of zero modes of $\psi_L$ and $n_R$ is the number of ...
4
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2answers
136 views
What is meant by “non-perturbative” string theory?
I often hear people talk about finding a non-perturbative formulation of string theory.
What does this mean exactly? To my knowledge string theory is a perturbative method. Just like Feynman graphs ...
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1answer
53 views
S Duality and Effective Couplings
I am brand new to this subject, so this will probably be a very stupid question, but I would appreciate any patient explanations.
S-duality is typically described as a relationship between two QFTs (...
22
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2answers
359 views
Can we get full non-perturbative information of interacting system by computing perturbation to all order?
As we know perturbative expansion of interacting QFT or QM is not a convergent series but an asymptotic series which generally is divergent. So we can't get arbitrary precision of an interacting ...
4
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1answer
97 views
Is there any proof that any result from perturbation theory is necessary an asymptotic series?
I know that almost all the series coming from perturbation theory are divergent, such as those from eigenvalue problems or the S-matrix in quantum field theory. The lore is that the series are ...
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0answers
103 views
What is the problem of non-pertubative quantisation?
In reading books about quantisation, there is (sometimes hidden) the claim, that quantisation is done using a pertubative approach. You look at the free field, find that it is essentially a sum of ...
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1answer
201 views
What's the difference between a gauge theory with group $G$ and one with its universal cover?
Consider a gauge theory with gauge group $G$, which is not simply connected. What is the difference between this theory, and one with gauge group $\tilde G$, the universal cover of $G$?
Sharing the ...
4
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1answer
145 views
How to path-integrate over the half-line?
Consider the path-integral over a scalar field $\varphi$:
$$
Z=\int_{\mathcal S}\ \mathrm e^{iS[\varphi]}\mathrm d\varphi
$$
where $\mathcal S$ is some function space (say, Schwartz or its dual).
How ...
13
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1answer
337 views
Why do we care about old-style, counterterm renormalizability?
There are a few different definitions of renormalizability that are standard in quantum field theory textbooks. They're all called the same thing, but I'll make up names to make the distinctions clear....
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1answer
210 views
How does 11D Supergravity relate to M-Theory?
I know Type IIA/B, Type I, HO, & HE are related through the T and S Dualities. However, how does SUGRA factor in here? What exactly is 11D SUGRA’s significance in M-Theory?
Some seem to suggest ...
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Non-perturbative quantum field theory textbook suggestion [duplicate]
I need resources preferably a thorough text book for non-perturbative quantum field theory. Please suggest good reads. Also lectures, lecture notes will help as well.
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2answers
286 views
What do we mean when we say 't Hooft proved that Standard Model is renormalizable?
This question is inspired from Why should the Standard Model be renormalizable? Ron Maimon says that standard model is renormalizable, and though there seems to be conflicting (?) answers. Is this ...
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Question about the vacua of the Standard Model
This question is probably based on a misunderstanding. Please correct me if I'm wrong, and if unclear, I'll try to put it in a clearer language.
In Yang-Mills theory such as the theory of strong ...
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2answers
218 views
Determination of the global structure of the SM gauge group
The Standard Model of particle physics can be constructed by specifying its gauge group $G$ and the representations of the fields (plus some extra information: Lorentz invariance, values of the ...
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0answers
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The role of the renormalization scale in the functional renormalization group
On p. 28 of Bertrand Delamotte's Introduction to the Nonperturbative Renormalization Group he writes
$k$ [the renormalization scale] acts as an infrared regulator (for $k \neq 0$) somewhat similar ...
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3answers
475 views
Books on non-perturbative phenomena in quantum field theory
I am looking for any good places (preferably textbooks) to study about introductory non-perturbative phenomena in Quantum field theory.
Any suggestion will be appreciated.
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What is the current situation about triviality of $\phi^4$ theory in $d=3+1$?
I was reading a book by Franco Strocchi, this one, and in some points the author claims that the case of $d=3+1$ of triviality of $\phi^4$ theory is now proven. As far as I can tell, we have just some ...
2
votes
2answers
308 views
Effects of Topological Terms: Hopf, $\Theta$, Chern-Simons, WZW, Berry phase term
What are the effects and the differences of Topological Terms?
For example, I had known and heard several of them are called Topological,
(1) Hopf term,
(2) $\Theta$ term,
(3) Chern-Simons term,...
22
votes
3answers
3k views
Does QED really break down at the Landau pole?
In QED, the fine structure constant $\alpha$ runs upwards in the UV, with a loop calculation (involving a geometric series of the vacuum polarisation diagram) indicating a divergence in $\alpha$ at $\...
2
votes
1answer
130 views
Baryon number violation in the Standard model at the perturbative and non-perturbative level
This is a continuation of my question here.
Page 635 of this book by Matthew Schwartz effectively says that the $\partial_\mu J^\mu_B\neq 0$ where $J^\mu_B$ is the baryon current i.e., the baryon ...
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1answer
61 views
Non-Perturbative effects QCD and the Standard Model?
I read in an article that the Standard Model leaves unanswered questions about the non-perturbative effects of the QCD.
I have basic knowledge about the perturbative and non-perturbative QCD. Could ...
3
votes
2answers
227 views
Why is the WKB tunneling amplitude a non-perturbative result?
The tunneling amplitude obtained from WKB aprroximation is given by $$|T(E)|=\exp\Big\{-\frac{1}{\hbar}\int\limits_{x_1}^{x_2}dx[2(V(x)-E)]^{1/2}\Big\}[1+O(\hbar)]$$ where $x_1$ and $x_2$ are the ...
3
votes
2answers
119 views
Is renormalizability only a problem in perturbation theory?
As far as I know, renormalization is needed when a scattering amplitude is divergent at some order of the coupling constant in a perturbation theory. So my question is whether the divergence (and thus ...
5
votes
2answers
456 views
Are perturbative and non-perturbative QCD both signs of new physics?
I was studying about quarkonia systems and reached this page at CERN Courier. Here, I came across the following text:
While the failure to reproduce an experimental observable that is ...
4
votes
2answers
424 views
Meaning of perturbative and non-perturbative renormalizability
What is meant by a theory to be (1) perturbatively renormalizable, (2) perturbatively non-renormalizable, (3) non-perturbatively renormalizable, and non-perturbatively non-renormalizable? In each case,...
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1answer
256 views
Is the non-perturbative approach to QFT a path integral approach? If so then how, given we don't have simple path integral formula for Dirac equation?
Here is my understanding of the scenario. Please correct me if i go wrong somewhere.
Initially, the perturbative approach to QED (Feynman diagrams) was very successful. But the same approach to QCD ...
5
votes
1answer
302 views
Why is the temporal gauge $A_0=0$ so popular in discussions of non-perturbative effects?
Almost every discussion of non-perturbative effects in Yang-Mills theory mentions in passing that they work in the temporal gauge. Why is this the case?
A good example is the QCD vacuum. Almost ...
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vote
1answer
110 views
Are all field interactions carried out through force-mediating particles?
To my knowledge, all field interactions are carried out through force-mediating particles. For example, electromagnetic interactions are carried out through exchanging photons. However, under the ...
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votes
2answers
848 views
Understanding typical non-perturbative calculations in QFT [closed]
Perturbative calculations in quantum field theory are based on S-matrix expansion and calculating the Feynman diagrams. These Feynman diagrams are related to the scattering cross-sections and decay ...
3
votes
1answer
139 views
Reference request for non-perturbative QCD
I am looking for some good books or lecture notes that discuss non-perturbative aspects of QCD such as: chiral symmetry and chiral symmetry breaking; the QCD phase transition and the QCD phase diagram;...
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1answer
350 views
On the asymptotics of interacting correlation functions
Consider an interacting QFT (for example, in the context of the Wightman axioms). Let $G_2(x)$ be the two-point function of some field $\phi(x)$:
$$
G_2(x)=\langle \phi(x)\phi(0)\rangle
$$
Question: ...
3
votes
0answers
223 views
Perturbative coupling for QFT
I'm confused about the definition of a perturbative coupling for QFT that it should be less than 4 $\pi$, because the higher order corrections comes of order $\lambda/(4 \pi)$ ..
Now why QCD is not ...
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votes
0answers
177 views
Higher category theory, renormalization, and non-perturbative QFTs
I'm (vaguely) aware of certain uses of higher category theory in attempts to mathematically understand quantum field theories -- for example, Lurie's work on eTQFTs, the recent-ish book by Paugam, and ...
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0answers
244 views
Non-perturbative approach to QFT in Hamiltonian formalism?
A simple conceptual question today: is it true that QFT can only be approached in a non-perturbative way only through the functional methods (like 1/N), while in the Hamiltonian formalism we can only ...
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votes
2answers
375 views
Mass Renormalization: Geometric Series of One Particle Irreducible Diagrams
Pretty much everywhere I look it is stated that the full two point Green function (let's say for the Klein-Gordon field) is a geometric series in the one particle irreducible diagrams, ie. in momentum ...
4
votes
1answer
92 views
Why do we have to sum the expansions around all the action's stationary points?
This is in some sense a follow-up question to my previous question Why is it OK to keep the quadratic term in the small $\hbar$ approximation?. I understand how we can expand the action around a ...
4
votes
1answer
87 views
Experimental observation of non-perturbative effects
Many quantum field theories come with non-perturbative objects such as solitons and instantons, and non-perturbative effects such as the Schwinger effect. However, it is hard to find any review on ...
5
votes
1answer
137 views
Is CP problem the problem?
I've heard an argument that the question of smallness of QCD $\theta$ parameter is called the problem (namely, strong CP problem), since the other dimensionless couplings (like $\alpha_{s}$), are of ...
5
votes
2answers
140 views
Why cannot a fundamental string couple to the R-R gauge field $C_{\mu\nu}$?
People usually say that D-branes can carry R-R charges, or can couple to R-R sector gauge fields. But why a fundamental string cannot couple to a 2-form R-R sector gauge field? What's the essential ...
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0answers
177 views
Some questions about QCD [closed]
About QCD, I have two questions. I know I should propose one question one time, but they are actually two steps of the same question: Non-perturbative aspects of QCD.
1, Why do we need to solve QCD ...
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votes
2answers
365 views
Why are CFT descriptions of String Theory inherently perturbative and how can it be circumvented?
Field theories like QED/QCD are a priori non-perturbative theories. Perturbatively you can describe them by Feynman diagrams which essentially sum over all topologies of virtual particle creation and ...
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0answers
33 views
Does an instanton couple equally to all flavors?
Do gravitational / electroweak / QCD / ... instantons couple equally to all fermion flavors? For example, do QCD instantons distinguish between the different quark flavors?
Edit, due to comment (...
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votes
1answer
105 views
Nonperturbative corrections that can break SUSY
I am puzzled by a statement that is made regarding non-perturbative corrections breaking supersymmetry.
Specifically, consider a one-dimensional system, described by the Hamiltonian
$$H = \frac{1}{2}...
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1answer
98 views
Non-perturbative Brane effects
In Johnson's Book about D-branes he gets the Tension of a D brane:
$$\tau_p = \frac{\sqrt{\pi}}{16 \kappa_0 g_s}(4\pi^2\alpha')^{(11-p)/2}$$
By performing a string amplitude calculation and ...
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1answer
302 views
How do we calculate the S-matrix using non-perturbative QFT?
The cross section of a scattering process in $QFT$ is computed in terms of the S-matrix elements. In perturbative $QFT$, the same is done by computing the S-matrix elements by using Feynman ...
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votes
1answer
917 views
Baryon number violation in the Standard Model
Anomaly cancellation in the Standard model requires $B-L$ to be constant, which is done using perturbative diagrammatic expansion. Secondly, baryon number is conserved as an $U(1)$ global field ...
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0answers
72 views
Topological terms VEVs and ghosts
Suppose we have the Standard model, and we want to calculate with VEVs of topological susceptibilities of $SU_{L}(2), U_{Y}(1)$ and $SU_{c}(3)$ fields, which have the form
$$
\tag 1 \kappa \equiv \...
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votes
2answers
1k views
What are non-perturbative effects and how do we handle them?
Schwartz's QFT book contains the following passage.
To be precise, total derivatives do not contribute to matrix elements in perturbation theory. The term
$$\epsilon^{\mu\nu\alpha\beta} F_{\mu\...
