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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Implications of Instanton Corrections (to Degenerate Vacuua) for Spontaneous Symmetry Breaking

We consider that if the classical vacuua of a theory are degenerate then each of them can be non-invariant under one or more of the symmetries of the Lagrangian. We can choose one of the vacuua and ...
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23 views

Perturbative series in physics: why are coeffcieints of Gevrey-1 type (i.e. bounded by $\alpha C^n(n!)^1$

I have only been able to find this explicitly mentioned in this paper on resurgence techniques in physics. And have chased up the hints it gives, but they are not very explanatory. Essentially, the ...
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33 views

What is the difference between real and complex instantons (mathemtically, and their physical significance), and connection to Wick rotation

I am struggling to understand the difference and physical significance between real and complex instantons- I think these are also sometimes called ghost instantons? There are also anti-instantons. ...
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Kallen-Lehmann representation and branch cuts at threshold masses

Let us consider the Kallen-Lehmann representation for the two-point function of scalar fields $$ \langle \Omega | T\left\{\phi(x) \phi(y)\right\}|\Omega\rangle = \int \frac{d^4 p}{(2\pi)^4} e^{ip\...
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60 views

Occurances of integrals of the form $Z(\lambda) = \int g(x)e^{-\frac{f(x)}{\lambda}}dx$ (and perturbation techniques) [closed]

I am writing a review on perturbation techniques (actually hyperasymptotic techniques) for integrals of the form $$Z(\lambda) = \int g(x)e^{-\frac{f(x)}{\lambda}}dx,$$ where the interest is in the ...
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48 views

Nonperturbative results for $\phi^3$ theory in dimensions $d>6$?

The theory is nonrenormalizeable in those dimensions, but can you say anything about the theory anyway? Specifically I am wondering about the status of whether the theory is trivial, i.e. a ...
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1answer
68 views

Non-renormalizeable Interaction Implies Trivial Interaction?

It has been rigorously proved that the $\phi^4$ theory is trivial, i.e. is a generalized free field, in spacetime dimensions $d>4$. It is also the case that this theory is non-renormalizeable in ...
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1answer
83 views

Nonrelativistic Quantum Mechanics Results Implying Analogous QFT Results?

One particularly fascinating example of this I have found is the following. The delta function potential has no effect in nonrelativistic quantum mechanics in spatial dimensions greater than or equal ...
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2answers
134 views

Triviality of Yang Mills in $d>4$?

It has been proved that the $\phi^4$ theory is trivial in spacetime dimensions $d>4$. By trivial I mean that the field $\phi$ is a generalized free field, or in other words, it's only nonzero ...
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38 views

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, ...
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1answer
219 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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65 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 ...
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3answers
284 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
61 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 (...
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2answers
435 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 ...
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1answer
111 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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111 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
259 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 ...
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1answer
153 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 ...
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1answer
429 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
287 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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2answers
368 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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110 views

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
234 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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50 views

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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635 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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210 views

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 ...
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2answers
403 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,...
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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 $\...
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1answer
148 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
70 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 ...
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2answers
313 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 ...
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2answers
140 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 ...
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2answers
482 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 ...
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2answers
570 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
340 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 ...
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1answer
395 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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1answer
119 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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2answers
965 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 ...
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1answer
159 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
366 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: ...
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250 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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205 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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269 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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501 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 ...
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1answer
99 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 ...
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1answer
96 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 ...
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1answer
157 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 ...
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2answers
182 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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202 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 ...