# Is a commutator a scalar?

[A,B] = AB-BA, so the commutator should be a matrix in general, but yet
[x,p]=i*hbar...which is just a scalar. Unless by this commutator, we mean i*hbar*(identity matrix) ?

I am asking because I see in a paper the following:

tr[A,B]

Which I interpret to mean the trace of the commutator [A,B]. But if [A,B] is just a scalar, then trace of a scalar should always just be the scalar..

Yes, in this case ##i \hbar## is shorthand for "##i \hbar## times the identity operator."

Ohhh ok thanks!! I can't believe I went through all of Griffiths and this point was never made clear.

dextercioby