Questions tagged [solitons]
Solitons are self-stabilizing solitary wave packets maintaining their shape propagating at a constant velocity. They are caused by a balance of nonlinear and dispersive (where the speed of the waves varies with frequency) effects in the medium.
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Dimension analysis in Derrick theorem
The following image is taken from p. 85 in the textbook Topological Solitons by N. Manton and P.M. Sutcliffe:
What I don't understand from the above statement:
why $e(\mu)$ has minimum for ...
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Type I' String theory as M-theory compactified on a line segment?
I was considering the S-dual of the Type I' String theory (the solitonic Type I string theory).
That is the same as the S-dual of the T-Dual of Type I String theory. Then, that means both length ...
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Does the existence of Higgs imply the existence of Magnetic Monopoles?
I am aware that in theories with spontaneous symmetry breaking, Magnetic Monopoles can exist as topological solitons. Can the same be done with the Standard Model gauge group. I am familiar with the ...
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Derrick’s theorem
Consider a theory in $D$ spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form
$$L= \frac{1}{2} G_{ab}(\phi) \partial_\mu \phi_a \partial^\mu \phi_b- ...
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Vortex in D dimensions soliton
let us consider
the two-dimensional configuration shown in Fig. 3.1a. The lengths of the arrows
represent the magnitude of φ, while their directions indicate the orientation in
the $φ_1 -φ_2$ plane. ...
user12906
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Domain wall and kink solutions from solitions equations
A general solition equation can be obtaion from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{92.6}$$
where $x_0$ is a constant of integration when we drived this ...
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Solving the soliton equation without energy
In this passage from Srednicki's Quantum Field Theory (page 576)
The solution of interest is time independent, so we can set $\dot\varphi = 0$. We can also rewrite the remaining terms in $E$ as
\...
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Potential in Relativistic Scalar Field Theory
My intention is to establish a Soliton equation. I have cropped a page from Mark Srednicki page no 576.
I have understand the equation (92.1) but don't understand that how they guessed the ...
user12906
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Valid theory in all dimensions for solitary waves
I'm studying soliton (solitary waves). They are many theory which explain the phenomenon, like sine-Gordon model. But sine-Gordon model has limitations when it applies to 4 dimension because it is ...
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Do instantons support quantum bound states?
When one quantizes a scalar in the 1+1 dimensions in the kink background of a double well potential, one finds a spectrum that includes: (1) a zero mode corresponding to the classical particle ...
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Oscillon and soliton
I want to know the major difference between oscillon and soliton in terms of radiating energy with respect to time and position. And what about their localization?
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Are QFT solitons expected to represent standard model particles? Or strings?
Is work on solitons in QFT's focused on finding solutions that could represent the fundamental particles of the Standard Model, or is the work focused on finding particles Beyond The Standard Model? ...
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Asymptotic limit of the two kink solution of the sine-gordon equation
I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as:
$$\phi=4\arctan\left(\frac{\sinh\frac{1}{2}(\theta_1-\theta_2)}{(a_{12})^\frac{1}{2}\cosh\frac{1}{2}(\...
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Significance of massive states in string theory
A free superstring has an infinite tower of states with increasing mass. The massless states correspond to the fields of the corresponding SUGRA. In "Quantum Fields and Strings: A Course for ...
Squark
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Could this model have soliton solutions?
We consider a theory described by the Lagrangian,
$$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$
The corresponding field equations are,
$$(i\...
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