# Why does the non-linearity of the string action prohibit stretching due to strong excitations?

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From 't Hooft's String Theory lecture notes (paraphrased):

To understand hadronic particles as excited states of strings, we have to study the dynamical properties of these strings, and then quantize the theory. At first sight, this seems to be straightforward. We have a string with mass per unit of length $T$ and a tension force which is also $T$. Think of an infinite string stretching in the $z$-direction. The transverse excitation is described by a vector $x^{\text{tr}}(z,t)$ in the $x y$-direction, and the excitations move with the speed of sound, here equal to the speed of light, in the positive and negative $z$-direction. This is nothing but a two-component massless field theory in one space-, one time-dimension. Quantizing that should not be a problem. Yet it is a non-linear field theory; if the string is strongly excited, it no longer stretches in the $z$-direction, and other tiny excitations then move in the $z$-direction slower. Strings could indeed reorient themselves in any direction; to handle that case, a more powerful scheme is needed.

I understand that the field theory is nonlinear, but what does that have to do with stretching the string with strong excitations?

Also, why does he mention that the string could reorient itself? Does this have to do with nonlinearity or just that the endpoints of the string are not fixed in this simplistic model?

Any help is greatly appreciated.

This post imported from StackExchange Physics at 2015-03-08 11:26 (UTC), posted by SE-user 0celo7
asked Mar 4, 2015

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