- #1

- 970

- 3

## Main Question or Discussion Point

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] ?