Degrees of Freedom of an electron

In summary, the conversation discusses the degrees of freedom of an electron, which has 2 degrees of freedom for spin up/down. However, the wave function for an electron is a 4 component spinor with complex components, resulting in a total of 8 independent elements. The conversation also mentions the inclusion of the positron, which also has 2 degrees of freedom, bringing the total to 4. It is recommended to not refer to the Dirac field as a "wave function" and to think of it as a classical wave equation.
  • #1
Neitrino
137
0
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
 
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  • #2
Stupid question ? :(
 
  • #4
Neitrino said:
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.
 

1. What does "degrees of freedom" refer to in relation to an electron?

"Degrees of freedom" refers to the number of independent variables that can affect the motion of an electron. In other words, it is the number of ways an electron can move or change its state in a given system.

2. How many degrees of freedom does an electron have?

An electron has three degrees of freedom: translational, rotational, and vibrational. This means it can move in three dimensions, rotate around its axis, and vibrate in different modes.

3. What factors determine the degrees of freedom of an electron?

The degrees of freedom of an electron are determined by the physical properties of the system it is in, such as the number of dimensions, the presence of external forces, and the type of interactions with other particles.

4. How does the concept of degrees of freedom relate to the behavior of electrons in a solid?

In a solid, electrons are bound to the atoms and have limited degrees of freedom due to the strong interactions with neighboring atoms. This leads to collective behavior of electrons, resulting in phenomena such as conductivity and magnetism.

5. Can the degrees of freedom of an electron be changed?

Yes, the degrees of freedom of an electron can be changed by altering the properties of the system it is in. For example, by applying a magnetic field, the rotational and vibrational degrees of freedom of an electron can be affected, leading to changes in its behavior.

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