The Nambu-Goto Action

  • Thread starter wam_mi
  • Start date
80
0
Hi there,

Recently, I read that the Nambu-Goto action of a free relativistic string is motivated from the study of the relativistic point particle moving sweeping out a world-line parameterised by the proper time. May I ask

(i) Why do we parameterise the world-line of the particle by the proper time? Is it because we want to ensure that the relativistic point particle action remains Lorentz invariant? How important is that?

(ii) A free relativisitc string sweeps out a world-sheet that is parameterised by one time-like and one spatial parameter. Then we can write the action in flat space. But what happens when we have to work in a general curved space-time? How are we sure we are allowed to work with the flat metric, and all the results later (e.g. light-cone gauge quantisation, Virasoro algebra, etc) in flat space-time agrees with that of the general metric?

In other words, how can we assume that flat metric is equivalent to general metric? Has this got something to do with conformal field theory?

Thanks!
 

Want to reply to this thread?

"The Nambu-Goto Action" You must log in or register to reply here.

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
Top