# Homework Help: Is this soliton ?

1. Feb 4, 2006

### panchan

Code (Text):

$$f_{\mu}=\frac{\beta_{\mu}\psi\xi_{_{g}}}{\cosh^{2}\psi\xi} ,\hspace{2em} \xi=\xi_{_{T}}x^{0}+\xi_{_{S}}\sqrt{(x^{1})^{2}+(x^{2})^{2}+(x^{3})^{2}} ,\hspace{2em} \beta_{\mu},\:\xi_{_{g}}},\:\xi_{_{T}},\:\xi_{_{S}}\rightarrow constant$$

Is this f_{\mu} soliton ?

Last edited: Feb 4, 2006
2. Feb 7, 2006

### marlon

I don't think many people will be able to help if you are not gonna try to be a bit more clear. Elaborate on the context surrounding your question, please. Whithin what course are you seeing this ?

As far as i remember, you acquire a soliton solution (in 2+1 dimensional QFT) if your solution gives you a constant value at infinity (both + and - infinities) and if in between, there is a continuous evolution from the "minus-infinity constant" towards the "+ infinity constant". Both constants are equal in magnitude but have opposite signs and they correspond to the socalled "vacuum value" (degenerate lowest energy value).

Here's more

marlon

3. Feb 21, 2006

### Kalimaa23

Thanks Marlon! Good link.