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.

Filter by
Sorted by
Tagged with
17
votes
1answer
899 views

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 ...
5
votes
2answers
289 views

Erik Lentz's faster-than-light soliton

It's well known that, in relativity, if you can go faster than light, you can go backwards in time and create a paradox. Also, attempts to create "warp-drive" space-times in which something ...
8
votes
2answers
652 views

No monopoles in the Weinberg-Salam model

I'm reading Chapter 10.4 on the 't Hooft-Polyakov monopoles in Ryder's Quantum Field Theory. On page 412 he explains why magnetic monopoles cannot appear in the Weinberg-Salam model. I'm I right by ...
3
votes
1answer
1k views

difference between classical vacuum solutions and instantons

What does the classical vacuum of the $SU(2)$ Yang-Mills action correspond to? Does it correspond to $F_{\mu\nu}=0$ everywhere or just at the spatial infinity? In Srednicki’s book, he has shown that, ...
2
votes
1answer
546 views

M branes/D branes are solitons?

I'm really confused. In M theory/String theory, the fundamental objects are M/D branes. However, branes by defintion are just solitons. Solitons are just waves that maintain there shape. So if a ...
5
votes
1answer
1k views

Distinction of Dirac monopole and Polyakov-'t Hooft monopole

Can anybody explain the physical difference between Dirac monopole and Polyakov monopole? First, let me write down what I know briefly. Dirac monopole It comes from the symmetry of Maxwell ...
2
votes
3answers
339 views

Describing travelling waves carrying energy from one point to another

A simple harmonic wave in one-dimension (for simplicity) $y(x,t)=A\sin(\omega t-kx)$ in a medium is often presented as an example of a travelling wave. But such a plane wave is infinitely extended ...
25
votes
1answer
1k views

Causes of hexagonal shape of Saturn's jet stream

NASA has just shown a more detailed picture of the hexagonal vortex/storm on Saturn: http://www.ibtimes.com/nasa-releases-images-saturns-hexagon-mega-storm-may-have-been-swirling-centuries-1496218 ...
3
votes
2answers
975 views

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- ...
28
votes
2answers
916 views

$\phi^4$ theory kinks as fermions?

In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \...
14
votes
1answer
902 views

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\...
8
votes
2answers
2k views

What is the definition of soliton?

What is the definition of soliton? I've encountered this name in different situations like when the topic discussed is about QFT, fluid dynamics or optics, but I cannot find a general definition. I've ...
6
votes
0answers
1k views

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? ...
4
votes
1answer
857 views

What is the intuition for topological currents?

The reason for topological stability of a kink solution in scalar field theory in $1+1$ dimensions is the fact that the finite energy scalar field cannot be continuously deformed into a vacuum. How ...
12
votes
2answers
4k views

Explanation of the waves on the water planet in the movie Interstellar?

We will ignore some of the more obvious issues with the movie and assume all other things are consistent to have fun with some of these questions. Simple [hopefully] Pre-questions: 1) If the water ...
3
votes
2answers
206 views

Why Kink can not tunnel to vacuum, and is topologically stable?

Why the kink $$\phi(x)=v\tanh(\frac{x}{\xi}) ,$$ can not tunnel into vacuum $+v$ or $-v$ (Spontaneous symmetry breaking vacuum). From the boundary condition ($x\rightarrow \pm\infty, \phi(x)\...
6
votes
1answer
231 views

Theory on domain walls

In Baryons in Quantum Chromodynamics, Zohar Komargodski have slide: I wanna understand: Why domein wall can have nontrivial worldvolume theory? When such solitonic objects have interior degrees of ...
2
votes
2answers
322 views

Nomenclature clarification concerning solitons

My experience with solitons is restricted to the classical setting, namely solutions to the quartic interaction $\phi^4$, the Sine-Gordon equation, and Korteweg–de Vries equations. I was explicit to ...
1
vote
1answer
477 views

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 ...
1
vote
1answer
305 views

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 \...