wam_mi
Apr5-10, 05:20 PM
Hi there,
I recently read about the construction of the Nambu-Goto action by looking at the proper area of the world-sheet. However, when one varies the action with an arbitrary space-time coordinate (here I treat it in Minkowski space-time X^(\mu)), there appears three terms and some of them would go to zero.
What I don't understand is why is that
(i) The momentum density running along the string P^(\mu)_(\sigma) at the open string endpoints \sigma (0, \pi) is zero?
(ii) Why is it that the momentum density transverse to the string, i.e. P^(\mu)_(\tau) \neq 0?
Has this got something to do with the conservation law, that energy is conserved?
Thanks
I recently read about the construction of the Nambu-Goto action by looking at the proper area of the world-sheet. However, when one varies the action with an arbitrary space-time coordinate (here I treat it in Minkowski space-time X^(\mu)), there appears three terms and some of them would go to zero.
What I don't understand is why is that
(i) The momentum density running along the string P^(\mu)_(\sigma) at the open string endpoints \sigma (0, \pi) is zero?
(ii) Why is it that the momentum density transverse to the string, i.e. P^(\mu)_(\tau) \neq 0?
Has this got something to do with the conservation law, that energy is conserved?
Thanks