![]() ![]() Proceedings of the National Academy of Sciences of the United States of America, 57, 194. An Analysis of the Structure of Space-Time. Journal of Mathematics and Physics, 8, 345. Proceedings of the Royal Society, A284, 159. Null Hypersurface Initial Data for Classical Fields of Arbitrary Spin and for General Relativity. Progress of Theoretical Physics (Kyoto), 11, 441. Progress of Theoretical Physics (Kyoto), 9, 147. The Principles of Quantum Mechanics, 4th ed. Proceedings of the Royal Society, A155, 447.ĭirac, P. Annales de l'École Normale Supérieúre, 31, 263.ĭirac, P. Comptes Rendus de l'Académie des Sciences, 248, 1782.Ĭartan, E. Mathematische Annalen, 94, 119.īruhat, Y. John Wiley and Sons, New York and London.īrinkmann, W. In: Gravitation: an Introduction to Current Research, ed. Proceedings of the National Academy of Sciences of the United States of America, 9, 1.įor further references and details, see Bhlers, J. American Journal of Mathematics, 57, 425.īrinkmann, W. On this view, curvature arises whenever a ‘shift’ occurs in the interpretation of the twistor variables Z α, \(\bar Z_\alpha\) as the twistor ‘position’ and ‘momentum’ operators, respectively.īrauer, R. It is suggested that twistors may supply a link between quantum theory and space-time curvature. The twistor expressions for the charge and the mass, momentum and angular momentum (both in ‘inertial’ and ‘active’ versions, in linearised theory) are also given. For this purpose, the Hubert space scalar product is described in (conformally invariant) twistor terms. The correspondence is then shown to be, in fact, valid for the Hubert space of functions f( Z α), which give the above twistor description of zero rest-mass fields. This suggests the correspondence \(\bar Z_\alpha = \partial /\partial Z^\alpha\) as a basis for quantization. The shifting of complex structure is naturally described in terms of Hamiltonian equations and Poisson brackets, in the twistor variables Z α, \(\bar Z_\alpha\). ![]() The C-picture still exists, but its complex structure ‘shifts’ as it is ‘viewed’ from different regions of the space-time. The effect of conformai curvature in the M-picture is studied by consideration of plane (-fronted) gravitational ‘sandwich’ waves. The twistor formalism is adapted so as to be applicable in curved space-times. By requiring that the singularities of f( Z α) form a disconnected pair of regions in the upper half of twistor space, fields of positive frequency are generated. In terms of twistor space ( C-picture) it is analytic structure which takes the place of field equations in ordinary Minkowski space-time ( M-picture). The four complex variables Z α are the components of a twistor. ), in terms of an arbitrary complex analytic function f( Z α) (homogeneous of degree −2 s −2). The formalism of twistors is employed to give a concise expression for the solution of the zero rest-mass field equations, for each spin (s=0, 1/2, 1. ![]()
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