D O C U M E N T 8 0 M A R C H 1 9 2 1 6 5
quence here that H [and] hence I and L would vanish there; I:L becomes undefined,
which appears to me to be an entirely reasonable result and can be understood
roughly in the sense that a physics founded on becomes immaterial there.
For n 4 there are analogous constructions; however, they are either of higher order
in the differential quots. or else they still contain variables. Generalizing in various
directions would therefore be possible; whether they are also necessary, I do not
know.
I and L are, in fact, different, because the term appears
in I, but not in L. After calculation, L is
Invariants that can occur as action functions in Weyl’s formulations have been sys-
tematically examined by
Weitzenböck.[5]
These examinations are appearing immi-
nently in our Academy—insofar as the immediate scheduling allows.
I am already very much looking forward to your so kindly promised news about
the “ ”-free
physics.[6]
Many thanks and respectful regards from your sincerely devoted
Wirtinger.
80. From Jakob Grommer[1]
[Göttingen or Berlin,] 5 March
1921[2]
Dear Professor!
Of the 4 invariants: I) ,
II) , III) ,
IV) , I = 4. II = numerical factor · and
III = IV = 0, in the centrally symmetric case. By the way, H. Wirtinger’s informa-
tion for is not right.[3] There the products of the derivatives of a, or of
, are omitted. It is like this:
H
H1212
2 g11g22 g12
–
2
1
g
-- -( H1212H3434 H2323H1414 H3131H2424
2 H1223H3414 H1231H3424 H1224H3431 H2331H1424 H3114H2324 H1214H3423 + + + + +
H1234
2
H3124
2
H2314
2
.
+ +
+
+ + +
HiklmHi'k'l'm'
iki k
g
------------ ----------------
lml m
g
HiklmHi
k l m
klk l
g
------------ ----------------
imi m
g
HiklmHi
k l m
1-
g
------ iki k gll gmm
HiklmHi
k l m
1-
g
------ klk l gii gmm HiklmHiklm
Riklm
1 a + =