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 + =