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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Formalizing Quantum Field Theory [duplicate]

I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or ...
27
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1answer
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Instantons, anomalies, and 1-loop effects

A symmetry is anomalous when the path-integral measure does not respect it. One way this manifests itself is in the inability to regularize certain diagrams containing fermion loops in a way ...
26
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5answers
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Why should the Standard Model be renormalizable?

Effective theories like Little Higgs models or Nambu-Jona-Lasinio model are non-renormalizable and there is no problem with it, since an effective theory does not need to be renormalizable. These ...
22
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3answers
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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 $\...
22
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2answers
419 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 ...
18
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1answer
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The Origins of Instantons from Path Integrals

I know that you can come across non-perturbative effects in QFT, particular when the coupling constant lies outside the radius of convergence of the asympototic perturbation series. From the ...
15
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1answer
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What's the relation between perturbative and nonperturbative QFT?

In case of any miscommunication let me describe my understanding of the meaning of "perturbative" and "non-perturbative", and correct me if something is wrong: In a perturbatively defined QFT the ...
14
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2answers
814 views

Non-Perturbative Feynman diagrams?

The Wikipedia page for Feynman Diagrams claims that Thinking of Feynman diagrams as a perturbation series, nonperturbative effects like tunnelling do not show up, because any effect that goes to ...
14
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3answers
967 views

How do we know that nonperturbative canonical quantum gravity is wrong?

In these forums and elsewhere it is routinely agreed that "we do not have a theory of quantum gravity." My question is, how do we know that canonical quantum gravity is "wrong"? I understand that the ...
14
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1answer
421 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....
12
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2answers
4k views

What does a non-perturbative theory mean?

I'm a science writer and I'm having difficulty understanding what a non-perturbative approach means. I thought I understood what perturbative meant, but in looking for explanations of non-perturbative,...
12
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2answers
230 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 ...
12
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1answer
364 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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3answers
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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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2answers
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Advanced topics in string theory

I'm looking for texts about topics in string theory that are "advanced" in the sense that they go beyond perturbative string theory. Specifically I'm interested in String field theory (including ...
9
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4answers
489 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 ...
8
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1answer
352 views

Do we need new physics to supercede triviality?

I've been reading about the higgs triviality bound (see for example here). It is discussed that the higgs self coupling at some energy scale becomes non-perturbative. If the higg's mass is above about ...
7
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2answers
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QCD in the non-perturbative regime

In the list of unsolved problems in physics. Confinement: the equations of QCD remain unsolved at energy scales relevant for describing atomic nuclei. How does QCD give rise to the physics of nuclei ...
7
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2answers
934 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 ...
6
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2answers
623 views

Why are many physicists trying to develop non-perturbative quantum theories? [closed]

I would like to briefly know where (and why) does perturbation theory fail and why are physicists so desperate looking for non-perturbative theories. (No Mc A, it's not obvious to me, is it not ...
6
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2answers
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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\...
6
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1answer
510 views

How do instantons look in real time/spacetime?

Instantons, as I understand it, are mathematical constructions in Euclidean spacetime. Does it imply that instantons do not exist in real spacetime or the instanton tunneling effects does not have ...
6
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0answers
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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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0answers
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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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0answers
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LSZ reduction theorem derivation in Weinberg QFT

When deriving LSZ reduction theorem Weinberg in his QFT book have assumed n-point generalized Green functions, $$ G(q_{1},...,q_{n}) = \int d^{4}x_{1}...d^{4}x_{n}e^{-i\prod_{i =1}^{n}q_{j}x_{j}} \...
5
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2answers
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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 ...
5
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2answers
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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 ...
5
votes
1answer
209 views

Separation of perturbative and non-perturbative contributions in partition function computation

The following is defined, where $\epsilon \to 0^+$ is a cutoff: $$ \mathcal{F}(Z)=\int_{\epsilon}^\infty \frac{\mathrm{d}s}{s} \frac{1}{\sinh^2 s/2} e^{-sx}. $$ Question: how do we see that $\mathcal{...
5
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1answer
245 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 ...
5
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0answers
196 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 ...
4
votes
2answers
346 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 ...
4
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2answers
413 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 ...
4
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3answers
253 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 ...
4
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2answers
537 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,...
4
votes
1answer
98 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
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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 ...
4
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1answer
103 views

Continuum of lattice QCD is free?

I am having a hard time getting to grips with the statement that $$g_{0}(a) \to 0 \text{ as } a \to 0$$ where $g_{0}$ is the bare coupling in lattice QCD and $a$ the lattice spacing. How come this ...
4
votes
2answers
224 views

What constitutes a 'reliable' instanton calculation?

In Modern Supersymmetry, John Terning, on pgs 151, and 153 performs a so called 'reliable' instanton calculation when dealing with the ADS superpotential 'since the gauge group is completely broken'. ...
4
votes
1answer
249 views

Mathematical proof that $\exp(-1/|g|)$ is always related with formation of bound states through scales?

I know that this function ($g$ means coupling) is non-analytical in $g=0$, so this function is only appreciable under non-perturbative calculations, so is a non-perturbative phenomena. This function ...
4
votes
1answer
88 views

Solitonic nature of RR sources

In the famous paper by Polchinski where he shows that D-branes are sourcing RR fields, he says (before we known the result) that RR sources must be objects with tension going like $1/g_s$ (page two of ...
4
votes
1answer
325 views

Do people confuse all-order perturbation theory with non-perturbative physics in QFT?

I've heard about people talking about the 1/N expansion as a mothod of nonperturbative QCD. This seems strange. In the 1/N expansion all you have is Feynman diagrams, which are by definition ...
4
votes
1answer
327 views

String matrix models with c>1

Question 1: What is the status of string random matrix models (~ triangulated random surfaces) with c>1? In my limited search, I have just come across a few papers by Frank Ferrari (in 2000-2002) on ...
4
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1answer
80 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 ...
4
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1answer
110 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 ...
4
votes
1answer
152 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 ...
4
votes
1answer
369 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 ...
4
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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 ...
4
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0answers
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 ...
4
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0answers
265 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 ...
4
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0answers
195 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 ...