In Weinberg's QFT Vol. 1 he says the Dirac equation is not a true generalization of Schrodinger's equation, that it does not stand up to inspection when viewed in this light. He says it should be viewed as an approximation to a true relativistic quantum field theory of photons and electrons. a) I do not understand what this means, would someone mind filling me in? One of Dirac's motivations for his derivation was that Klein-Gordon was not first order in time like the non-relativistic Schrodinger equation is. b) Since the 2'nd order in time Klein-Gordon equation does actually describe something physical.does this mean Dirac's point about not being first-order in time is actually flawed? From browsing Cartan's Spinor's book it seems the Dirac equation holds for any spinor, it apparently relates left & right representations of a spinor or something, thus it holds in GR etc... There is also this great quote from Atiyah that a spinor is a square root of a geometry. c) What is the Dirac equation & how does this explain why Dirac's derivation worked, why it relates representations of a spinor & explains this square root of a geometry business?