Single particle levels enumerated by n. States, where {tuv}={123} = particle labels, organized so as to result in the regular representation ():

n |
1 |
2 |
3 |
4 |
5 |
6 |

tuv |
123 |
312 |
231 |
132 |
321 |
213 |

One of the six representation matrices of the altered scrutiny of permutation.

Find so the reduced matrix is

State has property , that any permutation returns the same state so if have bosons only one state is admissable; the one that transforms as γ=1.

State produces ±1 on even/odd permutation; fermions

The transformation matrix between irrep states, |γjk>, of the system and states, |n>, of the system

December 2014

Marvin Chester

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