Line vortex(strings)

  • Thread starter ChrisVer
  • Start date

ChrisVer

Gold Member
3,328
437
I am just trying to understand a little bit the concept behind this, but I feel lost.

If we have the lagrangian:
[itex]L= (D_{μ}Φ)(D^{μ}Φ^{*}) - \frac{1}{4} F_{μν}F^{μν}+ V(|Φ|^{2}) [/itex]
with V being the Higg's Potential we can try to put as a solution of the dynamic system the relation:
[itex]Φ(x)= ρ(r) e^{iθn2π} [/itex]
This solution causes "problems" in the vacuum, because each winding of Φ stores up some energy.

One question I have about it, is why is this the case? I understand that in the covariant derivatives, terms of [itex]∇_{θ}[/itex] will give additional energy proportional to the winding number n. But isn't the Φ field U(1) invariant? So I can make U(1) transformations which will cancel out the exponential factor giving me the Goldstone boson dof as longitudial dof of the gauge bosons?

Also, any good book from which I can look up for Domain walls, these cosmic strings and GUT monoples would be appreciated :)

Thanks
 

Want to reply to this thread?

"Line vortex(strings)" You must log in or register to reply here.

Related Threads for: Line vortex(strings)

  • Posted
Replies
2
Views
3K
  • Posted
Replies
4
Views
4K
  • Posted
Replies
7
Views
4K
Replies
2
Views
1K
Replies
5
Views
2K
Replies
4
Views
6K
Replies
6
Views
5K
Replies
1
Views
729

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top