Note to the derivation of Dirac equation

[exponent137]

In book Quantum Electrodynamics, Feynman wrote that the Dirac equation is a relativistic form of the Pauli equation, not a correct form of Klein-Gordon equation. But, I think that the electron spin is only assumed in Pauli equation, but Dirac equation derives it?
I went through derivation in Feynman book, but somewhere I found something better. I do not find it now. It tries to linearize Klein-Gordon equation and so it obtains Dirac equations. Do anyone know any link? Why linearization is necessary? Why \gamma matrices are the only option? (I need to think to ask more concretely, because I think that there is more simple explanation.)

 

[Bill_K]

exponent, The discovery of the Dirac equation was a lucky accident. Historically, people tried first to use the Klein-Gordon equation, and encountered two surprises. One, the equation seemed to imply the existence of negative energy states. Second, it came with a continuity equation, but the conserved quantity was not always positive. Dirac tried to find an alternative equation, guessing it would be a first-order matrix equation. Imposing Lorentz invariance, he was led to the Dirac equation. (Notice I did not say "derive"!) He was not expecting it to describe a particle with spin.

Since then, we've realized that the Klein-Gordon equation, properly interpreted, is perfectly valid. The negative energy states must be replaced by antiparticles, and the conserved quantity is a charge density, not a probability density.

 

[exponent137]

And how it is with derivation of spin with the Pauli equation? Is it enough for derivation, or we need relativistic, Dirac equation that all parameters are fullfiled?

Pauli equation is generalized Schrodinger equation, including spin.

 

[dextercioby]

In book Quantum Electrodynamics, Feynman wrote that the Dirac equation is a relativistic form of the Pauli equation, not a correct form of Klein-Gordon equation.

It's true.

But, I think that the electron spin is only assumed in Pauli equation, but Dirac equation derives it?

In both equations, the properties of uncommuting objects (matrices) describing spin 1/2 are derived, not assumed.