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Miklós Schweitzer
2012 Miklós Schweitzer
6
6
Part of
2012 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 2012 P6
Source: Miklós Schweitzer 2012 P6
8/20/2018
Let
A
,
B
,
C
A,B,C
A
,
B
,
C
be matrices with complex elements such that
[
A
,
B
]
=
C
,
[
B
,
C
]
=
A
[A,B]=C, [B,C]=A
[
A
,
B
]
=
C
,
[
B
,
C
]
=
A
and
[
C
,
A
]
=
B
[C,A]=B
[
C
,
A
]
=
B
, where
[
X
,
Y
]
[X,Y]
[
X
,
Y
]
denotes the
X
Y
−
Y
X
XY-YX
X
Y
−
Y
X
commutator of the matrices. Prove that
e
4
π
A
e^{4 \pi A}
e
4
π
A
is the identity matrix.
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