Advances in Twistor Theory by L. P. Hughston, R. S. Ward

By L. P. Hughston, R. S. Ward

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I analytic massless wave function. a htistor function may be found (by way of the inverse twister function ) ". eous ly (which may be arbitrarily and "2 \'J; "rough" and for which the con'esponding twistor function's domain may need to be al'bi trar'i 1y narrow ) . HO\~ever. i sets fOI' our sheaf cohomology (and there seems no reason against this), then the covering of PT+ by the 35 two closed sets , given respectively by z'L Z, .! tL i: ~ 0 0 and by " will suffice (as the inver-se twistor function sho~ls) for (j 'j' such \~ave functions .

Space can be represented by space . ed on some ideas introduced by Rawnsiey (1979); Hitchin (1979); and Eastwood, PenrOse & h'ells (1979). A more detailed account of the Penrose Uansform using forms rather than sheaf cohomology can be found in Wells {1979} . 2. shall use the follol-ling notation: M+ is the fOflolat"d tube of (comrIex) ~'inkowski space , T+ '" {z':I ; ZQy' > OJ is the corresponding (nonprojective) " half tl'listor space, and B+ is the bundle of primed spinors over H+; t-+ ++ -+ -+-+ 0 : B -.

F'"J"' assigned to J (/ ; n Uj n Uk ; . and r ij = . f j i , fUk = - f jik = f jk ; = . e. 26 .. f 1. . 1 The n Ii. . I I-cochain 6 :: (f 12 , '23,'13" " ) 2-cochai n 1 = ( f I23 " 124 " " ) (where U1 I' U2 , U2 n tl3 ' II I f'I u 3 ' , ·,. U1 n U2 ' U3 , til r, U2 " are the non- empty intersectio ns of 01 's). I:,;a /,y opl: ra to"l' t. as follows: "f" "f" 12 "f" 23 13 , ~ • (fI 2- fI3+f23 ' f I2- fI4+f 24 ···· ) "f 123" "f 124" etc . (where . aqa in, (II " tl2' .. , ,2 • O. We ca 11 y a fa" some •• H~U,, \ cC<'Jjr::l l' Define the p "e thf!

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