Commutator
Definition
[
A
,
B
]
=
A
B
−
B
A
Properties
If
[
A
,
B
]
=
0
then
A
and
B
commute
[
A
,
A
]
=
0
[
A
,
a
]
=
0
[
A
,
B
]
=
−
[
B
,
A
]
Linearity:
[
A
,
B
+
C
+
D
]
=
[
A
,
B
]
+
[
A
,
C
]
+
[
A
,
D
]
[
A
,
B
C
]
=
[
A
,
B
]
C
+
B
[
A
,
C
]
Jacobi Identity:
[
A
,
[
B
,
C
]
]
+
[
B
,
[
C
,
A
]
]
+
[
C
,
[
A
,
B
]
]
=
0
If
A
,
B
are Hermitian and
A
B
is Hermitian then
[
A
,
B
]
=
0
.
Anticommutator
{
A
,
B
}
=
A
B
+
B
A
Author: Christian Cunningham
Created: 2024-05-30 Thu 21:18
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