All Questions
Tagged with solitons field-theory
7
questions
4
votes
2
answers
1k
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
$$L= \frac{1}{2} G_{ab}(\phi) \partial_\mu \phi_a \partial^\mu \phi_b- ...
user12906
2
votes
1
answer
643
views
Dimension analysis in Derrick theorem
The following image is taken from p. 85 in the textbook Topological Solitons by N. Manton and P.M. Sutcliffe:
What I don't understand from the above statement:
why $e(\mu)$ has minimum for ...
- 651
15
votes
1
answer
993
views
Could this model have soliton solutions?
We consider a theory described by the Lagrangian,
$$\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\...
- 1,714
9
votes
2
answers
4k
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 ...
- 1,193
4
votes
1
answer
1k
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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 ...
- 17.8k
3
votes
2
answers
328
views
Why can kink not tunnel to the vacuum, making it topologically stable?
Why can the kink
$$\phi(x)=v\tanh\left(\frac{x}{\xi}\right)$$
not tunnel into vacuum $+v$ or $-v$ (with spontaneous symmetry breaking in the vacuum)?
From the boundary condition, $\phi(x)\rightarrow \...
- 49
3
votes
1
answer
212
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In which representation are monopoles of grand unifying theories classified?
In the context of grand unification theories A.Zee's book states that $SU(5)$ (or $SO(10)$ if $SU(5)$ is considered as outdated as GUT candidate) as GUT and as spontaneously broken non-abelian gauge ...
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