# Permutation operator

1. Nov 16, 2007

### cks

1. The problem statement, all variables and given/known data

I can't really imagine how this was approached.

Let $$P_{\alpha0}$$ fixed

$$P_{a0}A=\frac{1}{N!}\sum_{\alpha}\epsilon_{\alpha}P_{\alpha0}P_{\alpha}=\frac{1}{N!}\epsilon_{\alpha0}\sum_{\alpha}\epsilon_{\beta}P_{\beta}=\epsilon_{\alpha0}A$$

2. Relevant equations

3. The attempt at a solution

I can understand that $$P_{\alpha0}P_{\alpha} = P_{\beta}$$ is a new permutation operator.

$$P_{a0}A=\frac{1}{N!}\sum_{\alpha}\epsilon_{\alpha}P_{\alpha0}P_{\alpha}=\frac{1}{N!}\sum_{\alpha}\epsilon_{\alpha}P_{\beta}$$

Last edited: Nov 16, 2007
2. Nov 16, 2007

### Hurkyl

Staff Emeritus
What do all of your symbols mean?