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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Non-perturbative approach to high-energy physics

I know that main numerical approach to modeling high-energy particle physics events are Monte-Carlo event generators. But they are using perturbative description of collision and decay processes of ...
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Can the Functional Renormalization Group not generate a flow that is generated perturbatively?

I think I might have stumbled on a calculation that appears to undergo renormalization when you compute it perturbatively, but not when you compute it using the FRG. Consider, for the sake of argument,...
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Area and perimeter

Apparently (?), a line operator over a very large loop with length $L$ can obey either perimeter law or area law, $-\log\langle U\rangle\sim L^a$ with $a=1,2$, respectively. We call these options &...
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Evolution operator as a Laurent series of coupling constant

Let the Hamiltonian be $H_{0}+gV$, where $g$ is the coupling constant. In the interaction picture, the equation for the evolution operator is $i\frac{dU}{dt}=gV_{I}U$. What I am going to do is assume $...
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Should the $S$-matrix always analytic in coupling constant?

If we use Dyson series, the $S$-matrix is always an analytic function of the coupling constant. However, if that is the case, how can non-perturbative effects arise in QFT? My question is, should the $...
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Is renormalization needed if non-perturbative approach of $S$-matrix works?

Assume there is a way to construct $S$-matrix in a non-perturbative way, is renormalization still needed in computing $S$-matrix? Since when I encounter regularization and renormalization, they are ...
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What is the difference between a perturbative and a non-perturbative vacuum?

What is the difference between a perturbative and a non-perturbative vacuum in quantum field theory? Is there an analog of these ideas in non-relativistic quantum mechanics?
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QFT's bound states references

At a graduate level, QFT courses teach very well how to perform perturbative calculations using LSZ or even the background field method. Plenty of books are suggested to go into the details of this ...
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Why is the chiral condensate a negative quantity?

The chiral condensate serves as an order parameter for the chiral phase transition. Thus, it is a finite quantity in one phase and vanishes in the other phase. It is given as a vacuum expectation ...
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Is QCD parity conserving also non-perturbatively?

Since QCD is fundamentally non-perturbative at low energies one may ask if QCD is still Parity conserving. In the path-integral formalism using the Faddeev–Popov ghosts as gauge fixing terms the ...
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Functional Renormalization Group and Dirac Fermions — Yukawa Theory

I've been practicing with FRG techniques and I wanted to obtain the usual beta functions for Yukawa theory using the Wetterich equation. However, this has been more troublesome than I expected. If I'm ...
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Can convergent perturbation series be incorrect for an action linear in the perturbation?

Non-perturbative effects are common in mathematics. For example, consider the function $$f(g) = e^{-1/g}+ g + \frac{1}{10} g^2$$ and suppose this function is the answer to some math problem. ...
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What are some good resources to learn about perturbative and non-perturbative approaches to QCD, for example Lattice QCD, at an introductory level?

I am writing at an introductory level about the anomalous magnetic moment of the muon and part of that is the subsequent Lattice QCD that potentially verifies the results from the experiments that ...
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Do Universal Spacetimes have Non-perturbative quantum corrections?

Universal spacetimes have the interesting property that their quantum corrections vanish to all loop orders, and can be viewed as classical solutions to speculative theories of quantum gravity like ...
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Did $\int dx^4 \partial ^\mu \phi(x) \partial_\mu \phi(x)= -\int dx^4 \phi(x) \partial^2 \phi(x)$ in the path integral formalism?

In the canonical quantization, one assumed the condition that the field $\phi(x)$ vanished at both space and time infinity. However, in the path integral formalism, thought the field $\phi(x)$ was ...
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Non-Perturbative Effects Of Soliton in Quantum Field Theory

I am reading Quantum Field Theory in a Nutshell by A.Zee. In Chapter 5 Section 6, Under the subtitle A nonperturbative phenomenon, He commented "That the mass of the kink comes out inversely ...
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Old-fashioned perturbation theory and contribution from resonances

In his QFT vol. 1 (paragraph 3.5), Weinberg discusses the so-called old-fashioned perturbation theory (OFPT), i.e. the one based on the perturbative expansion of the Hamiltonian. As a result, in this ...
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Physical interpretation of hadron distribution amplitudes

A parton fragmentation function can be interpreted as the probability that a final state hadron originated from that particular hadron. A parton distribution function can be interpreted as the ...
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How do we perform a perturbative expansion for magnetic monopoles?

Magnetic monopoles in non-abelian (and even abelian) gauge theory essentially appear as a non-perturbative, composite phenomenon if we perform the standard perturbative expansion in terms of, say, ...
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$SU(2)$ gauge SUSY with Affleck-Dine-Seiberg term

Consider SUSY gauge theory with $SU(2)$ group and matter fields $Q$ and $\bar{Q}$ in fundamental and anti-fundamental representations correspondently and the following superpotential: $$W=\frac{{\...
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$SU(2)$ gauge supersymmetric theory and superpotential

I am currently studying supersymmetry and I came across a superpotential of the following form $$W=\frac{\Lambda^5}{\bar{Q}Q}+m\bar{Q}Q.$$ The first term is said to appear as a result of non-...
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Chiral zero modes in type IIB matrix model

I have seen many articles in which the authors consider various modifications of IKKT matrix model (non-perturbative regularization of type IIB string theory) such as (Orbifolds, fuzzy spheres, ...
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When does QFT perturbation theory stop being valid?

When introduced to the concept of perturbation theory in Quantum Mechanics we split the hamiltonian $H= H_0 + \delta H$ where $\delta H$ is small in some manner, ie if say $\epsilon$ is the relevant ...
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Does quantum field theory exist non-perturbatively or is perturbation inherent to its Nature?

In quantum field theory, calculations generally are made by using a perturbation approximation with the aid of Feynman diagrams. The theory is not well suited for bound states as Feynman diagrams ...
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What is the difference between the perturbative renormalization group and the non-perturbative renormalization group?

In the context of quantum field theory, I often see non-perturbative RG associated with Wilson - I take it that this is what people usually mean when they simply say RG. What is the perturbative RG ...
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Renormalization in non-perturbative QFT ($n$-point function)

How does one do renormalization if one can exactly calculate the $n$-point function of QFT? Take for example QED when doing renormalization We calculate $2$ and $3$ point function Expand them in ...
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Do sum rules for spectral function always hold?

In condensed matter physics, we can define the spectral function as $$ A_{\alpha}(\omega) = -\frac{1}{\pi}\mathrm{Im}G_{\alpha}^R (\omega) $$ It can be shown that this quantity satisfies the sum rule: ...
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Hydrogen atom in quantum field theory

In principle, how would we demonstrate the existence of the hydrogen atom in quantum field theory and the standard model? Has it been done in practice? Some naive ideas: Demonstrate that the familiar ...
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What's the difference between operator product expansion and perturbation?

Operator product expansion and perturbation theory both looked somewhat similar to Taylor/Laurent series expansion. Quote: Conformal Field Theory, Philippe Di Francesco, Pierre Mathieu, David Senechal,...
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Canonical quantization

I am looking for a generic treatment or a concrete example where canonical quantization is performed without using free fields. For a scalar field $$\phi(x,t) \sim \sum_k \phi_k{(t)} \, u_k(x) + \...
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How is $\Lambda_{\textrm{QCD}}$ relevant in the non-perturbative regime?

The famous $\Lambda_{\textrm{QCD}}$ parameter enters through the one-loop running of the QCD coupling, through a relation similar to the following: $$\alpha_S(Q^2)=\frac{\alpha_S(Q^2_0)}{1+b\ln(Q^2/Q^...
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Is it possible to treat fermion reheating from inflaton decay only perturbatively?

In case of an inflaton Lagrangian $ \mathcal{L} = \frac{1}{2} (\partial_\mu \phi)^2 - \frac{1}{2}m_\phi^2 \phi^2 -h \overline{\psi} \phi \psi $ where the inflaton field is coupled only to fermions ...
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Are Green functions non-perturbatively infrared finite?

Are Green functions non-perturbatively infrared finite? In other words imagine one had the final form of the 4-point function for spin-1/2 field, do we still need infrared radiation correction? In ...
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Besides instantons and large-$N$ what are some other general non-perturbative methods for quantum field theory?

Besides large-$N$, instantons, lattice QFT, what are some other non-perturbative methods that help us better understand QFTs like the large distance dynamics of Yang Mills and QCD?
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QCD generating functional and QCD vacuum from nonperturbative to perturbative regime!

The complete generating functional in QCD (starting from the most general renormalizable, Lorentz invariant and gauge invariant Lagrangian) given by $$Z_\theta[J]=\int \mathcal{D}A \exp i\int d^4x~ {\...
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What's the difference between perturbative QCD, non-perturbative QCD, and gauge theory QCD?

I'm trying to get the ideal of QCD, and it turns out that there seems to be several versions, and some of which does not appear to agree with each other at a glance. What's the difference, and how ...
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9 votes
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Definition of dangerously irrelevant operator

(Disclaimer: There is already a question about dangerous irrelevant operators which has not been very successful. However, the question there is quite broad, and here I aim to ask a more precise ...
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1 vote
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Relation Asymptotic Series and perturbative effects

Perturbative expansions of a function $f(x)$ around say $x=0$ cannot determine contributions from a function such as $e^{-1/x}$ since its Taylor series vanishes to all orders. This kind of ...
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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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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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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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1 vote
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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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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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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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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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4 votes
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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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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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2 votes
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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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7 votes
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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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