All Questions
7
questions
0
votes
2
answers
126
views
$O(3)$ 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 $$\mathcal{L} = (1/4)\partial _{\mu}\phi \cdot \partial ^{\mu}\phi + \nu (1-\phi \cdot \...
user320803
2
votes
0
answers
67
views
How do you check the stability of a kink solution?
I am reading a nice introductory note by Hugo Laurell (http://uu.diva-portal.org/smash/get/diva2:935529/FULLTEXT01.pdf) but got confused on section 3.2.
He claims the stability of kink by expanding a ...
- 311
3
votes
1
answer
903
views
Finding the energy of a solution to the Sine-Gordon equation
I am delving into Quantum-Field Theory, and am stuck trying to work out how to compute the energy of a soliton solution to the Sine-Gordon equation in 1-1 spacetime.
I start with the Lagrangian ...
- 1,224
3
votes
2
answers
328
views
Why can kink not tunnel to the vacuum, making it topologically stable?
Why can the kink
$$\phi(x)=v\tanh\left(\frac{x}{\xi}\right)$$
not tunnel into vacuum $+v$ or $-v$ (with spontaneous symmetry breaking in the vacuum)?
From the boundary condition, $\phi(x)\rightarrow \...
- 49
3
votes
2
answers
342
views
Why is the solution of the $\phi^6$ potential not a soliton?
Consider a theory with a $\phi^6$-scalar potential:
$$
\mathcal{L} = \frac{1}{2}(\partial_\mu\phi)^2-\phi^2(\phi^2-1)^2.
$$
I solved its equation of motion but found that the general form of its ...
- 175
4
votes
2
answers
1k
views
Derrick’s theorem
Consider a theory in $D$ spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form
$$L= \frac{1}{2} G_{ab}(\phi) \partial_\mu \phi_a \partial^\mu \phi_b- ...
user12906
1
vote
1
answer
577
views
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