An Introduction to String Theory

Slide 32 of 37
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The behavior of the string's interior is the same in both the closed and open string cases. In fact, if you could look at a piece of a string "up close" so you couldn't see whether it looped back on itself or not, there would be no way to tell whether it was an open or closed string. That's good news for us, because it means much of our discussion of the closed string carries over directly to this case.

If anything, the open string is a simpler case because we do not need to keep track of "left-moving" and "right-moving" waves separately: because the waves bounce off the ends of the string, the two types mix freely. As before, the vibrational states carry both energy and polarization, so we will see them as particles of different mass and spin. The formula for energy as a function of momentum and vibrational level is similar to the closed string spectrum, and the massless states have N = 1, corresponding to the usual photon.