D O C . 4 5 9 F I E L D T H E O R Y & H A M I LT O N P R I N C I P L E 4 1 3 § 3. The Limiting Case of σ = 0 For carrying out the transition to the intended limiting case, we require some preparation. We can write G *μα in the form . (18) From (3) and (11a) follows that depends quadratically and homogeneously on the Sα μν . Furthermore, G *μα fulfills the identity . (5a) Now, according to (17a), the limit σ = 0 immediately yields the relation . (19) These 6 equations lead—apart from special cases—to the vanishing of the 4 quantities . In the following, I also assume that as a result of the transition to σ = 0, the quantities decrease toward zero proportionally to σ, which I, how- ever, have not been able to prove thus far. Eliminating from (18) and (17a), one obtains the equation , or, after carrying out the operation D μ , as a result of (5a), . (20) In taking the limit to σ = 0, the second term vanishes its numerator decreases to- ward zero as , that is, proportionally to , according to our above assump- tion, so that one obtains , (21) which equation, together with (22) comprise the result of this limiting case. We can view the combination of the systems of equations (9), (21), and (22) as the final result of this investigation, whereby the derivation of (21) is not completely rigorous. We note further that the equations (22) imply that instead of the Hamilton func- tion (7), the Hamilton function (7a) could just as well be used in equations (9). G * 1 2 --S /  H * + = H * D  *  G 0  S /  0 = [p. 159] S  S  S / 2 G * H * –  f  – 0 = D  f  2 H *  ------------- - +    0 = S    2 2 D  f    0 = S   0 = H J 1 J 3 – =