3
votes
0answers
72 views

Proof for the Mass gap of sine-Gordon action with $g \cos(\beta \Phi)$

This is the sine-Gordon action: $$ \frac{1}{4\pi} \int_{ \mathcal{M}^2} dt \; dx \; k\, \partial_t \Phi \partial_x \Phi - v \,\partial_x \Phi \partial_x \Phi + g \cos(\beta_{}^{} \cdot\Phi_{}) $$ ...
1
vote
1answer
231 views

What is the winding number of a magnetic monopole, and why is it conserved

I had asked a similar question about a calculation involving the winding number here. But i haven't got a satisfactory response. So, I am rephrasing this question in a slightly different manner. What ...
3
votes
1answer
94 views

Is the force between solitons with same charge always repulsive?

I know the one-dimensional case in which the force is proportional to $e^{-R}$ and the force is attractive for solitons with opposite charge and repulsive for solitons with same charge. I was ...