- #1
gonadas91
- 80
- 5
Hi ! I have a doubt about fermionic operators with the anticommutation relations. I know they follow anticommutation, that is,
\begin{eqnarray}
\lbrace c_{i}^{\dagger},c_{j}\rbrace=\delta_{i,j}
\end{eqnarray}
That is for fermionic operators. But, suppose I have two different kind of fermionic operators, i.e, one refers to the left "wire" of a system, and the other to the right "wire".
\begin{eqnarray}
c_{i, L}^{\dagger} c_{j,R}^{\dagger}
\end{eqnarray}
Here, L denotes that this fermionic operator act on the left wire of a system, while R means the right wire.
My question is, do this operators COMMUTE? I mean, because they are acting on different parts of a system (like a subsystem), do they commute? Iam getting confuse about it! The thing is, can I do this?
\begin{eqnarray}
[ c_{i,L}^{\dagger},c_{j,R}]=0
\end{eqnarray}
\begin{eqnarray}
\lbrace c_{i}^{\dagger},c_{j}\rbrace=\delta_{i,j}
\end{eqnarray}
That is for fermionic operators. But, suppose I have two different kind of fermionic operators, i.e, one refers to the left "wire" of a system, and the other to the right "wire".
\begin{eqnarray}
c_{i, L}^{\dagger} c_{j,R}^{\dagger}
\end{eqnarray}
Here, L denotes that this fermionic operator act on the left wire of a system, while R means the right wire.
My question is, do this operators COMMUTE? I mean, because they are acting on different parts of a system (like a subsystem), do they commute? Iam getting confuse about it! The thing is, can I do this?
\begin{eqnarray}
[ c_{i,L}^{\dagger},c_{j,R}]=0
\end{eqnarray}