Degrees of Freedom of an electron

[Neitrino]

Dear PF,
I have a question about degrees of fridom.

Electron is 1/2 spin particle so it needs 2 component wave function. But instead haveing 1 equation of second order we linearize and have two equations of order 1 for two spinors and these two equations can be re-written in one equation for 4 component spinor.

But this four component wave function has complex components ...and so there are eight independent elements in wave function.

What I am confused is that electron has degrees of freedom 2 (spin up/down) and wave function 8 ? correcct or what I don't understand? or complexity of wave function does not account in degrees of freedom?

Thanks
Nick

 

[Neitrino]

Stupid question ? :(

 

[malawi_glenn]

here is a good thread about spinors:
https://www.physicsforums.com/showthread.php?t=204531

 

[Ilja]

Electron is 1/2 spin particle so it needs 2 component wave function. But instead haveing 1 equation of second order we linearize and have two equations of order 1 for two spinors and these two equations can be re-written in one equation for 4 component spinor.

But this four component wave function has complex components ...and so there are eight independent elements in wave function.

What I am confused is that electron has degrees of freedom 2 (spin up/down) and wave function 8 ? correcct or what I don't understand?

There is also the positron, with its two degrees of freedom. Thus, we have four of them.

And for a single "degree of freedom" of a wave we need one second order or two first order equations.

I also recommend you not to name the Dirac field psi "wave function", and to ignore all texts which use such a naming convention. Think of the Dirac equation as a classical wave equation, as the analogon of the Maxwell equation for particles with spin 1/2.