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Questions tagged [non-perturbative]

Use this for questions which discuss models of quantum theories which do not make use of peturbation theory.

Use this for questions which discuss models of quantum theories which do not make use of peturbation theory.

E.g. , which are defined through .

162 questions
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Formalizing Quantum Field Theory

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 conformal field theories, and of older approaches…
user566
38
votes
1 answer

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 compatible with the symmetry. Specifically, it seems…
user6013
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37
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3 answers

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 $\sim 10^{286}\,\text{eV}$. It is often claimed…
gj255
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36
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2 answers

Can we get complete non-perturbative information of the interacting system by computing perturbation to all orders?

As we know, the perturbative expansion of interacting QFT or QM is not a convergent series but an asymptotic series that is generally divergent. So we can't get arbitrary precision of an interacting theory by computing higher enough order and adding…
maplemaple
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35
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5 answers

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 theories are valid until a scale $\Lambda$…
Leandro Seixas
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28
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1 answer

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. A theory is counterterm renormalizable if all…
knzhou
  • 107,105
24
votes
2 answers

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 zero faster than any polynomial does not affect the…
harold_sax
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23
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1 answer

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 perspective of canonical quantization I understand how and…
Edward Hughes
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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 fields are quantized as free fields, and the…
Jia Yiyang
  • 4,135
19
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2 answers

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, I'm just confused about both concepts. Please…
John Boyd
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3 answers

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 theory is perturbatively nonrenormalizable, but…
user1247
  • 7,509
18
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4 answers

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.
TheQuantumMan
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15
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2 answers

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 $$\epsilon^{\mu\nu\alpha\beta} F_{\mu\nu}F_{\alpha\beta}$$ is a total derivative. If we…
knzhou
  • 107,105
13
votes
2 answers

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 coupling constants, etc.). Using this model we can…
coconut
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13
votes
1 answer

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: What is known about the behaviour of $G_2^{-1}(p)$…
AccidentalFourierTransform
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