# Why does Dirac Equation describe spin 1/2 particles?

1. May 9, 2012

### bigbigtheory

Hi, Everybody!

Currently, I am reading the book "Lectures on Quantum Field Theory" (by Ashok Das)

But I am a bit confusing. Why does Dirac Equation describe spin 1/2 particles?
I have already known that Dirac Equation bears some angular momentum structure, but why it just describe spin 1/2 not others?

Best wishes.

2. May 10, 2012

### Seaumas

Please see: "Generalized total Angular Momentum Operator for the Dirac Equation in curved Spaced Time" by B. Carter in Physical Review, Vol. 19, No. 4, p. 1093-1097. The 1/2 spin relates to Dirac's eigenstructures. Feynman has a diagram about it you may find interesting.

3. May 10, 2012

### dextercioby

It's one of the wonders and puzzles of theoretical physics the fact that linearizing the K-G equation which properly describes spin 0 particles leads to an equation which describes spin 1/2 particles.

The answer to your "why" is simply <study the whole Dirac's argument>. Spin 1/2 follows naturally from angular momentum considerations, once the 4x4 dimensionality of the alpha/beta/gamma matrices has been proven.

Last edited: May 10, 2012