L. P. Hughston, R. S. Ward's Advances in Twistor Theory PDF

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

ISBN-10: 082248448X

ISBN-13: 9780822484486

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M. equations. form: 1 WAI (x) = ---2' TIl f AI f X ~TI. AI Differentiating, it is easy to verify that w is a Hertz potential for ¢A AI providing that iTIAlf = f. There is some freedom available in the specifiAI AI AI cation of f ,for the invariance of f under the transformation f ~ f AI + 1T 9 is readily ascertainable~ where g(Zu) is any holomorphic function I which is hom(-3). ,', " IV. rn. field, AI hence it follows that the freedom in f induces the proper gauge freedom AI a vail a b1e to t); ~ Twistor cohomology groups.

LQ. 38- 39. ' .. ;,;: J.. ;:' """'·':~e. 7', eds . J . Isham . R. 101. Sciama . 407. ~1acCallum. M. H. 1972 Phys. C . 241 - 315 . Strea ter . F. & Wightman , A. S . ;;;'- • •. -'. Penrose, R. & Benjami n: New Vork. :. 2 HliSTOR FUNCTIONS AND SHEAF COHOMOLOGY by R. l properties of a hlistor functio n f(ZCt ) , to be used for ~eneratin9 a zero rest-mass field :'A' . 2 r ' A' .. • , K(X) (211 0 - ? c: x ""fA 2 ~ ! 'x ". I'" , 2 L' f (2 " ) d r. 2) (nm' under the Poincan~ t~listoY' space )101- gr oup , nor the lorentz gr oup) .

X} becomes singular. nd Q n PT are diSjoint. A suitcble twistor function would be 21 Lx /l I I I I r / I /~ , / / PT Lx n S Figure A (6) j . k" n (m , l,j,k non-negative integers). e. consider the case n = m = 1 = j = k = O. The cDrrespondi ng As an illustration, A' (xl::: PA' t i xAA' P and Let p A ' qA' (x) = QA + i xAA'QA be the solutions of the twistor equation 0(A'w B ')=o corresponding, respectively, to the twistors P and Q (cf. Chapter 1), " " The contour integral (4) is easily evaluated in this case and yields the answer ~ I 'Arc'~'----­ p (x) qA' (x) " 22 (7) whe re za is the space - time po int cor re spo nding to the line lz '" P n Q, and Ie: is the constant 2(P A QA) -l .

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


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