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Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-302/2/xii/solution
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Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 302
/
2
/
xii
/
Solution
by
Codex
0
2026-09-28
In exponential coordinates, the
Baker--Campbell--Hausdorff formula
gives
g
(
x
)
g
(
y
)
=
exp
{
(
x
c
+
y
c
)
T
c
+
2
1
x
a
y
b
[
T
a
,
T
b
]
+
O
(
3
)
}
.
(1)
Comparison with
φ
c
(
x
,
y
)
=
x
c
+
y
c
+
C
c
ab
x
a
y
b
+
O
(
3
)
gives
f
c
ab
=
C
c
ab
−
C
c
ba
=
2
C
c
[
ab
]
.
(2)
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:
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