A First Course in String Theory

14.1 Counting bosonic states

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is the number of ‘s.

is the number of different ‘s.

For , .

(Indices and are not powers. Instead, they are just upper indices for representing different ‘s.)

When all ‘s commute, and , for example, represent the same state. So we have to avoid double-counting, except for the same ‘s states, such as .

By direct counting, without using the formula, the number of products of the form can be built is

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Let , the number of ways to put indistinguishable balls into boxes.

By using the formula, the number of products of the form can be built is

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— Me@2015-07-26 08:43:22 AM

2015.07.26 Sunday (c) All rights reserved by ACHK