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Spinors and space-time Roger Penrose, Wolfgang Rindler
Publisher: Cambridge University Press

The super Poincaré Lie algebra has, on top of the Lie algebra cocycles that it inherits from 𝔰𝔬 ( n ) , a discrete number of exceptiona cocycles bilinear in the spinors, on the super translation algebra, that exist only in very special dimensions. Alain Connes should appreciate ;-). Moreover, this chapter asserts that the usual classical views of space and time conceal deeper concepts and relations from which both the space-time and the fundamental physical interactions are formed. Making 4d space from just fermions! (And it is why gravitational waves — waves in space and time, massless just like light — can be formed by objects that are orbiting one another.) Simply put, the Einsteinian view of gravity (now reasonably well confirmed by experiment) .. This structure is very general. As well as any discussion of time without space becomes scholastic. Penrose explains the many details and twists of the notation in The Road to Reality and in his (and Rindler's) Spinors and Space-time I, where you'll find extensions to deal graphically also with spinors and twistors. In the Penrose program they are called twistors. Is that, covariant fermions and contravariant fermion (spinor) indices i see? The following theorem has been stated at various placed in the physics literature (known there as the brane scan for κ -symmetry in Green-Schwarz action functionals for super- p -branes on super-Minkowski spacetime). Second, both programs use two-component (complex) spinors (more precisely, pairs of two-component spinors) as the more primary entities. €�Spinors”, “trapped energy spheres in very tiny spaces”, once I even called them Fermi spheres which you quickly corrected me, thank you. In this post, I'd like to take some time to explain the term "field" as it is used in physics and many areas of mathematics. (very roughly speaking : a kind of gauge field "between" two copies of the usual four-dimensional space-time, carrying respectively massless left-handed and right-handed spinors). The authors start with fermion fields and vector spin connection, and build spacetime out of it. This volume introduces and systematically develops the calculus of 2-spinors. One account, simplified by the use of spinors, can be found in “Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields (Cambridge Monographs on Mathematical Physics)”. To convey, unsuccessfully (due to my poor use of the English language) here for some time. We see that the spinor propagator equals a scalar propagator, which provides the pole and time-order structure, multiplied by some matrix in spinor space.