All Questions
Tagged with solitons field-theory
42
questions
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99
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What is the topology of sine-Gordon equation?
In one pdf on solitons, I am finding the following written
For the sine-Gordon theory, it is much better to think of $\phi$ as a field modulo $2\pi$, i.e. as a function $\phi: R \rightarrow S_{1}$. ...
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Do topological solitons allow modeling non-degenerate multiple vacua?
I am not well-versed in the research on topological solitons but am interested to make a good sense of its implication.
The highly interesting point in this new talk by Nick Manton was where he is ...
- 487
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1
answer
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Scale transformation of the scalar field and gauge field
I am reading this paper: "Magnetic monopoles in gauge field theories", by Goddard and Olive. I don't understand some scale transformations that appear in Page 1427.
Start from the energy ...
- 1,421
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If principle $SU(N)$ bundles on 3-manifolds are trivial, how can there be magnetic monopoles?
Magnetic monopoles are solitons, i.e. field configurations on space (which is 3 dimensional). In pure $SU(N)$ gauge theory, magnetic monopoles can be constructed via 't Hooft's abelian projection (...
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Why are non-perturbative solutions important and how to take them into account?
I am guilty of studying physics with an almost complete focus on the mathematical constructions (together with the motivating physical premisses) and ignoring the semantic physical intuition, which I'...
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2
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$O(3)$ sigma model for lumps
I'm studying the $O(3)$ $\sigma$-model related to lumps through chapter 6 of Manton's book.
There appears that $$\mathcal{L} = (1/4)\partial _{\mu}\phi \cdot \partial ^{\mu}\phi + \nu (1-\phi \cdot \...
user320803
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How $\varphi^6$ potential of topological soliton kink and anti-kink are calculated?
how $\varphi^6$ topological soliton kink and anti-kink are calculated ?, what is an anti-kink?
$$L = -\frac{1}{4}F_{\mu\nu}^2− |\varphi|^6 − ieA_\mu(\varphi^\ast\partial_\mu\varphi−\varphi\partial_\mu\...
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1
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A primer on topological solitons in scalar field theories
As the title suggests I want to learn more about topological solitons in scalar field theories. I am searching for a resource which is self-contained, in the sense that it also explains the ...
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How do you check the stability of a kink solution?
I am reading a nice introductory note by Hugo Laurell (http://uu.diva-portal.org/smash/get/diva2:935529/FULLTEXT01.pdf) but got confused on section 3.2.
He claims the stability of kink by expanding a ...
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An instanton in $d$ dimensions is often a soliton in $d + 1$ dimensions?
The title of this questions is a "folklore" I've heard from a lot of researchers, but I never understood why this is the case. I know what an instanton and soliton is, respectively in the ...
- 713
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1
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What are the two different $\mathbb{S}^n$ in the construction of the homotopy group $\pi_n(\mathbb{S}^n)$ that classifies topological defects?
According to Mukhanov's Physical Foundations of Cosmology,
Homotopy groups give us a useful unifying description of topological defects. Maps of the $n$-dimensional sphere $\mathbb{S}^n$ into a ...
- 26.7k
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468
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How to Diagonalize Self-Interacting Scalar Hamiltonian for Mass Term from Polyakov Paper?
So, I'm reading through Polyakov's paper from 1974, "Particle Spectrum in Quantum Field Theory." I'm trying to work through all of the steps and properly understand everything. For context, ...
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3
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Stability and topological charge of kink (anti-kink) solutions (soliton)
I am reading the book << Gauge theory of elementary particle physics >>. In chapter 15, it presents a model having finite-energy solution.
First, we have a $1+1D$ spacetime model
\begin{...
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1
answer
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Must a field approach one of its vacua to have finite energy?
I'm reading these Cornell lectures on solitons (link doesn't work right now, but it just worked yesterday), and I can't seem to prove what I thought would be a simple analysis exercise.
Namely, ...
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Set of zeroes as coset space
I am currently studying Chapter 6 of Coleman S. - Aspects of Symmetry.
We study a spontaneously broken gauge theory in two spatial dimensions where the Lagrangian reads:
$$
\mathcal{L} = -\frac{1}{4}...
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