A First Course in String Theory

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13.6 Unoriented closed strings

This problem is the closed string version of Problem 12.12. The closed string with and fixed is a parameterized closed curve in spacetime. The orientation of a string is the direction of the increasing on this curve.

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Introduce an orientation reversing *twist* operator such that

Moreover, declare that

(b) Used the closed string oscillator expansion (13.24) to calculate

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Equation (13.24):

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By comparing with , we have:

— Me@2019-11-24 04:33:23 PM

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2019.11.24 Sunday (c) All rights reserved by ACHK