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Questions tagged [instantons]

An instanton (pseudoparticle) is a classical solution to the equations of motion, usually of Yang-Mills theory, with a finite, non-zero action, on a Euclidean spacetime. Instantons normally dominate the path integral of Y-M theory and determine its quantum tunneling behavior. May use for merons and other topological field-theoretic configurations.

An instanton (pseudoparticle) is a classical solution to the equations of motion, usually of Yang-Mills theory, with a finite, non-zero action, on a Euclidean spacetime. Instantons normally dominate the path integral of Y-M theory and determine its quantum tunneling behavior.

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The meaning of imaginary time

What is imaginary (or complex) time? I was reading about Hawking's wave function of the universe and this topic came up. If imaginary mass and similar imaginary quantities do not make sense in physics, why should imaginary (or complex) time make…
glebovg
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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 compatible with the symmetry. Specifically, it seems…
user6013
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Does the existence of instantons imply non-trivial cohomology of spacetime?

Gauge theories are considered to live on $G$-principal bundles $P$ over the spacetime $\Sigma$. For convenience, the usual text often either compactify $\Sigma$ or assume it is already compact. An instanton is now a "false vacuum" of the theory - a…
ACuriousMind
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What is the status of Witten's and Vafa's argument that the QCD vacuum energy is a minimum for zero $\theta$ angle?

The argument, which I reproduce here from Ramond's `Journies BSM', is originally by Witten and Vafa in ($\it{Phys}$. $\it{Rev}$. $\it{Lett}$. 53, 535(1984)). The argument is that for $\theta = 0 $ (mod $2\pi$) the QCD vacuum energy $E(\theta)$ is…
DJBunk
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How do instantons cause vacuum decay?

From what I read about on instantons (Zee, QFT in a Nutshell, pg 309-310), an instanton is a vacuum solution that maps $S^3 \rightarrow S^3$ (the boundary of Euclideanized spacetime), which comes from minimizing the Euclidean action for some…
physics_researcher
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Instantons and Non Perturbative Amplitudes in Gravity

In perturbative QFT in flat spacetime the perturbation expansion typically does not converge, and estimates of the large order behaviour of perturbative amplitudes reveals ambiguity of the perturbative expansion of the order $\exp(-1/g^2)$ where $g$…
user566
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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 perspective of canonical quantization I understand how and…
Edward Hughes
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How to understand "analytical continuation" in the context of instantons?

Since this is a subtle and interesting question to me. I will give a rather detailed description. I hope you can keep reading it and find it interesting too. For simplicity, in the following I will only discuss the one-dimensional instanton, that…
Wein Eld
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Why is a superposition of vacuum states possible in QCD, but not in electroweak theory?

There are two standard stories floating around in modern particle physics: Spontaneous symmetry breaking can only happen in a QFT, like in the electroweak theory, because no tunneling between the degenerate vacuum states of the scalar field are…
jak
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Instanton Moduli Space with a Surface Operator

I would like to understand the mathematical language which is relevant to instanton moduli space with a surface operator. Alday and Tachikawa stated in 1005.4469 that the following moduli spaces are isomorphic. the moduli space of ASD connections…
Satoshi Nawata
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Can massive fermions have zero modes?

I'm confused about fermion zero modes in relation to instantons. I understand that instantons can create fermion zero modes, but it's not clear to me when a fermion has a zero mode. For example, consider QCD with nonzero fermion masses: i.e. there…
Pengpeng Xu
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Why not regard all large gauge transformations as genuine ones?

A large gauge transformation is a gauge transformation that is not connected to the identity. When quantizing a gauge theory, we must take configurations related by ordinary gauge transformations to represent the same physical state, but it is…
knzhou
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Difference between instantons and sphalerons

What is the difference between instantons and sphalerons? If they are different, how do they violate baryon and lepton number in the standard electroweak theory?
SRS
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What is "localisation" of instantons?

I often encountered the term "localization" in the context of instantons, as for example in the work of Nekrasov on extensions of Seiberg-Witten theory to ${\cal N}=1$ gauge theories. Could someone give a "intuitive" explanation of the concept of…
bangnab
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Solving Quantum Tunnelling Without Wick Rotation

Edit It seems that I haven't written my question clearly enough, so I will try to develop more using the example of quantum tunnelling. As a disclaimer, I want to state that my question is not about how to perform a Wick rotation in the path…
Adam
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