- #1
RedX
- 970
- 3
If you have a Grassman number [tex]\eta[/tex] that anticommutes with the creation and annihilation operators, then is the expression:
[tex]<0|\eta|0>[/tex]
well defined? Because you can write this as:
[tex]<1|a^{\dagger} \eta a|1>=-<1| \eta a^{\dagger} a|1>
=-<1|\eta|1>[/tex]
But if [tex]\eta[/tex] is a constant, then shouldn't:
[tex]<0|\eta|0>=<1|\eta|1>=\eta[/tex] ?
[tex]<0|\eta|0>[/tex]
well defined? Because you can write this as:
[tex]<1|a^{\dagger} \eta a|1>=-<1| \eta a^{\dagger} a|1>
=-<1|\eta|1>[/tex]
But if [tex]\eta[/tex] is a constant, then shouldn't:
[tex]<0|\eta|0>=<1|\eta|1>=\eta[/tex] ?