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A new group of action functions in the unitary field theory. II

Published online by Cambridge University Press:  24 October 2008

L. Infeld
L. Infeld
Affiliation:
Lwów
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Extract

There exists a group of action functions, depending on a parameter γ giving for every γ ≥ 0 a static solution with central symmetry and finite energy, both for the electric and magnetic field, and going over into Maxwell's action function for weak fields. For γ = 1 we obtain Born's case distinguished by a perfect symmetry between electric and magnetic field. For γ = 0 the action function takes a particularly simple form and the comparison with the results of Heisenberg, Euler and Kockel allows of an approximate determination of the fine structure constant.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 33 , Issue 1 , March 1937 , pp. 70 - 78
Copyright
Copyright © Cambridge Philosophical Society 1937

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References

† Born, , Proc. Roy. Soc. A, 143 (1934), 144.CrossRefGoogle ScholarBorn, and Infeld, , Proc. Roy. Soc. A, 144 (1934), 425;CrossRefGoogle Scholar 147 (1934), 522; 150 (1935), 141.

‡ Infeld, , Proc. Camb. Phil. Soc. 32 (1936), 127,CrossRefGoogle Scholar quoted here as I.

§ p *kl,f *kl are dual to p kl, f kl.

∥ This will be done later in a separate paper written in collaboration with B. Hoffmann.

† The dependence of T on F, P, and not on F, P, R, does not form a restriction, since R can always be expressed as a function of F and P, viz. R 2 = − PF. These assumptions simplify the calculations but are not more special than those in I. There is another generalization, where T depends also on G and Q (cp. Proc. Roy. Soc. A, 144, 425Google Scholar), but we shall not consider it in this paper.

‡ We can safely assume here and later that R ≠ 0, since R = 0 leads to the exceptional case F = P = 0.

† The condition is: Hr 3 = 0 for r = ∞.

† Heisenberg, and Euler, , Zeits. für Phys. 98 (1936), 714;CrossRefGoogle ScholarEuler, and Kockel, , Naturwiss. 23 (1935), 246.CrossRefGoogle Scholar

‡ We omitted in (6·7) the term proportional to (which occurs in the formula of Euler and Kockel) since it arises from the dependency of L on the invariant which we did not assume.