Relation With Nambu-Goto Action
Writing the Euler-Lagrange equation for the metric tensor one obtains that:
Knowing also that:
One can write the variational derivative of the action:
where which leads to:
If the auxiliary worldsheet metric tensor is calculated from the equations of motion:
and substituted back to the action, it becomes the Nambu-Goto action:
However, the Polyakov action is more easily quantized because it is linear.
Read more about this topic: Polyakov Action
Famous quotes containing the words relation with, relation and/or action:
“There is undoubtedly something religious about it: everyone believes that they are special, that they are chosen, that they have a special relation with fate. Here is the test: you turn over card after card to see in which way that is true. If you can defy the odds, you may be saved. And when you are cleaned out, the last penny gone, you are enlightened at last, free perhaps, exhilarated like an ascetic by the falling away of the material world.”
—Andrei Codrescu (b. 1947)
“Any relation to the land, the habit of tilling it, or mining it, or even hunting on it, generates the feeling of patriotism. He who keeps shop on it, or he who merely uses it as a support to his desk and ledger, or to his manufactory, values it less.”
—Ralph Waldo Emerson (1803–1882)
“All real freedom springs from necessity, for it can be gained only through the exercise of the individual will, and that will can be roused to energetic action only by the force of necessity acting upon it from the outside to spur it to effort.”
—Anna C. Brackett (1836–1911)