692
DOC.
650
NOVEMBER
1918
650.
From
Felix
Klein
Göttingen, 10
November
1918
Esteemed
Colleague,
Your
postcard
of
8
November has
just arrived.[1]
Meanwhile,
with Miss Noe-
ther’s
help,
I
understand
that the
proof
for
the
vector
character
of
Ea
from
“higher
principles”
as
I
sought
was
given
by
Hilbert
on
pp.
6,
7
of his first
note,[2]
although
in
a
version
that
does not draw attention
to
the
essential
point.
The
specific
structure
of
K
is
not
used
there,[3]
rather K
can
be
any
invariant
formed
from
the
arguments coming
into consideration. In
the
following
manner:[4]
1)
At
the
start,
we
cut
away
from

or
rf,
respectively,
all
components
that
recognizably
have
the
desired vector character. There remains
(q=(
9pcr
for
investigation
of its nature.
2)
In
any case,
dc/dw2
is
an
invariant.[5] The
highest
term
(a
term
with the
highest
differential quotients
for
Puvp)
to
appear
in it
is:
-dk/dguvpuvpo.
3)
Now
we
have
the
obvious statement:
puv
transforms
(under
arbitrary
trans-
formation of
w) as a
tensor,
if
the
terms with
lower
differential quotients
are
disregarded.
This
is
enough
to
conclude
that-dk/dguv
that-dk/dguv
is
a
tensor,
which
now,
as
in
my
previous
letter, will
be called
Kpouv.[6]
4)
Once
we
finding,
we
set,
again
as
in
my
earlier
letter,
in
making
use
of
the
process
of covariant differentiation
P¡T
=
A?
+
T^p™
+
TuTppTp,
where
Auvp
is
now a
tensor.
5)
Accordingly,
-KpouvAuvg
is
a
regular
vector,
which
we
eliminate.
There
remains:
=
(
)puv
to
be
analyzed,
which
we
immediately
want
to abbreviate,
=
Bouvpuv.
6)
Then
it’s
the
same
game anew as
in
(1),
(2)
....
:
a)
In
any event,
do/dw
is
an
invariant.[7]
b)
The
highest
term to
occur
in it
is
B°uvpuvo.
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