By L. P. Hughston, R. S. Ward
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Extra info for Advances in Twistor Theory
P'Px F(Z ) ~D,d~ ] IPIA' ••• P' Tr W2A I ••• (3) PI; The left hand side of (3) could only be singular in S2' and the right hand side only in 51' so both sides must be globally holomorphic. Being homo- geneous of degree zero, they must therefore be independent of TI " by A a Liouville's theorem. Thus ¢B ... P' is a function only of x Similar ' arguments show that ¢B' ... PI is symmetric and satisfies the field equations. The procedure can also be applied to functions F(Zu) homogeneous of 47 I ,1 degree n > -2, as follows.
REFERENCES Griffiths, P. d Anatytic Geometry. Princeton University Press. C. 1966 Lectures on Niemann Sv:t~faces. Princeton University Press. Penrose, R. H. 56 1965 1966 Proc. Roy. Soc. A284, 159-203. Atgebraic Topology. McGraw-Hill.
E): Charge integrality in the "twisted photon" We have (Narrow & Kodaira 1971) the exact sequence o -. , O. where 0* refers to non - zel'o holomorphic functions taken multipl icatively, (rom which we derive the long exact sequence: 1 r •• ' AB= O 71 Al1 a f b. "twisted j photon" ordinary integer 1 s t cononlO 109Y Choose X as a I"e9ion in PT I ol'dinary integer 2nd cohomology correspondin<;l to a small space-time tube surrounding 11 cha r ge world - l ine. , 52 x R2. l) = O. Zl '" l e Z. Thus the space Hl(X,o w) effectively conta in s H1(X, O).
Advances in Twistor Theory by L. P. Hughston, R. S. Ward