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By Ivan T. Todorov

Those notes arose from a chain of lectures first provided on the Scuola Interna zionale Superiore di Studi Avanzati and the overseas Centre for Theoretical Physics in Trieste in July 1980 after which, in a longer shape, on the Universities of Sofia (1980-81) and Bielefeld (1981). Their aim has been two-fold. First, to introduce theorists with a few history in team representations to the suggestion of twistors with an emphasis on their conformal houses; a brief advisor to the literature at the topic is designed to compensate partially for the imcompleteness and the one-sidedness of our evaluation. Secondly, we current a scientific learn of po sitive strength conformal orbits when it comes to twistor flag manifolds. they're interpre ted as cl assi ca 1 section areas of "conformal parti cl es"; a characteri sti c estate of such debris is the dilation invariance in their mass spectrum which, there fore, is composed both of the purpose 0 or of the countless period 222 o

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Indeed. 1.. 4. 3. The symplectic form is fixed by 50 0(4,2) (~U(2,2)/Z2) invariance (and energy positivity) up to a (positive) factor. 37) [d and d standing for differentiation with respect to Z and Z, respectively; IT Z = 1 - (Z &Z/ZZ)l. 38b) According to the Darboux theorem for every symplectic form w there exist aanoniaaZ local aoordinates (qa,p~) such that w =dqaAdPa. e. the expression for the SU(2,2) generators Jab in terms of the z-variables. Every antisymmetric tensor Jab on PQ is proportional to i(ZaZb -ZbZa)/ZZ.

29) 50 0(2,2) xSO(2) being the stability subgroup of the point z =(0,0,0,0) [or Z =(0,0, O,i,l,O)], which corresponds to the bivector f -e: (-,+) = (cr 1 -cr 1 e:) (-1)aa (0)o . ~) (~) A ). Its stability subgroup is the 8-dimensional group generated by Finally, the most degenerate 4-dimensional orbit, corresponding to z =0, is isomorphic to the real compactified Minkowski space M. 0. O) = (i) {i) ). 6. 45). 4 Higher Flag Manifolds We turn to a brief description of the 5(complex}-dimensional flag manifolds F1 ,2 and F1 ,3.

51 The knowledge of the ladder (and anti ladder) representations of U{2,2) provides us with a tool for constructing man'ifestly lorentz covariant local O-mass fields. To fix the ideas we shall speak about (second) quantized fields. 18) [and ~ is a vector in the representation space of V, so that (V~)a =v~~a]. ~(x) is local if its components commute or anticommute for spacelike separations (depending on whether 2s is even or odd). ) The study of an arbitrary ~ of the above type can be brought to the investigation of its irreducible components.

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