Problem 14.1b

A First Course in String Theory
 
 
14.1 Counting bosonic states

~~~

Let N(n, k) = {n + k - 1 \choose k - 1}, the number of ways to put n indistinguishable balls into k boxes.

p.318 “For open bosonic strings \alpha' M^2 = N^\perp - 1, …”

 
When \alpha' M^2 = 3, N^\perp = 4, the cases are: 

1. four a_1^\dagger‘s:

N(4,24) = 17550

2. one a_2^\dagger and two a_1^\dagger‘s:

24 \times N(2,24) = 24 \times 300

3. two a_2^\dagger‘s:

N(2,24) = 300

4. one a_3^\dagger and one a_1^\dagger:

24 \times 24 = 576

5. one a_4^\dagger:

24

 
Total number of possible states for N^\perp = 4 is 25650.

— Me@2015-08-13 12:05:57 PM
 
 
 
2015.08.13 Thursday (c) All rights reserved by ACHK