# Field of one fermion

1. May 1, 2004

### Marjan

One thing is bothering me from "the beginning".

Let's take one fermion. It has spin, charge and mass (of course).

This particle is surrounded with static magnetic field (becouse of it's spin), and with static electric field (becouse of it's charge).

Both field (separately) are represeneted as virtual photons in S.M. Well, for el. field we need another fermion close to this one, but that is not a problem.

So, what is the difference beetween those two kinds of photons? Spin?

And another question: Why do we need to accelerate this fermion that we get electromagnetic field?? What happens with those two kinds of virtual photons that we get real photons?
If those fields before were static, E.M. is dynamic (oscilation of those two fields...), right?

2. May 3, 2004

### Haelfix

What you want is a field theory interpretation.. Ie one quantum field. Now, for the one fermion field, there is a very old and elegant solution to this, and its called the Dirac lagrangian. Its a free field theory, but it possesses all the things you know and love (charge, spin, etc etc). If you solve the equations of motion, you get the Dirac equation, from there in the nonrelativistic, hbar --> 0 case, you get Maxwells equations.

Upon quantizing this field, you get some of the things you are talking about, eg virtual photons (in essence they are perturbation series artifacts, and not necessarily physical depending on how you like to think of them).

Virtual photons, are identical to real photons, except that they live off mass shell.

3. May 3, 2004

### Marjan

Haelfix, congrats for 100 post on PF :)

I agree with you.
Well I say that virtual photons are the same as real, they just exist so short time that it is not possible to meassure them. Is this the same as your state "they live off mass shell" ?

Well I tried to understand my first post here, so I did homework.

I took an electron, and I calculated magnetic moment:

p = g*e*L/2*m, where g is approximately 2 and L=sqrt(s(s+1))hbar.
This is a source of static magnetic field H or B. But how do I calculate it?

But I meet with problem when I try to calculate electric momentum, which should be a source of static electric field. I can only calculate electric moment for two particles: p = e l, where l is distance between them.

Did I meet with "monopole - dipole" problem?

How do I calculate electric field of single particle?

If I done any mistake, I would be glad if you express it.

4. May 7, 2004

### Marjan

I think it's very interesting subject, becouse here we come to fundamental source of magnetic and electric field...