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.
- I do not understand what this means, would someone mind filling me in? (Assuming he's saying something more general & subtle than merely saying Dirac is not a one-particle equation)
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.
- 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, and that Dirac's equation worked for some other reason?
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.
- 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?