ar X iv : h ep - t h / 03 04 26 5 v 1 3 0 A pr 2 00 3 Dirac ’ s Footsteps and Supersymmetry

I am not interested in proofs. I am only interested on how Nature works P.A.M. Dirac One hundred years after its creator's birth, the Dirac equation stands as the cornerstone of XXth Century physics. But it is much more, as it carries the seeds of supersymmetry. Dirac also invented the light-cone, or " front form " dynamics, which plays a crucial role in string theory and in elucidating the finiteness of N = 4 Yang-Mills theory. The light-cone structure of eleven-dimensional super-gravity (N = 8 supergravity in four dimensions) suggests a group-theoretical interpretation of its divergences. We speculate they could be compensated by an infinite number of triplets of massless higher spin fields, each obeying a Dirac-like equation associated with the coset F 4 /SO(9). The divergences are proportional to the trace over a non-compact structure containing the compact form of F 4. Its nature is still unknown, but it could show the way to M-theory. Much of modern physics starts with the Dirac equation. Its deceptively simple form γ α p α Ψ = p / Ψ = 0 , (1) obscured the significance of the simple algebraic relation for its anticommutator { p / , p / } = p 2. (2) Today we understand this as the seed of supersymmetry, which could be called protosupersymmetry. In the context of string models, this relation turned out to be very potent. There, the momentum was generalized to a momentum density along the string P α (σ) = p α + oscillators , (3) suggesting that the momentum operator is the average of the momentum density p α = < P α > .