# Spin Potential: If spin is really a fundamental property like a charge or mass, then Is there a potential associated to spin?

I am sorry for not having added the details initially , This is my first Question on physics stack Exchange.

This thing croped up in my mind from the ideas of fermi holes and fermi heaps, The basic thing is that two non interacting opposite spin particles connot occupy the same state. Now ,In the coordinate space, I think this means that they cannot occupy the same position.But what can we assume the effective distance which they have to mantain to see themselves as "not in same position". Now if there is such a effective distance then would that mean we have essentially a potential for the spin interaction.

Also, Maybe I am terribely wrong but , isnt the justrow factor in computational physics their to compensate for such an interaction??

• My guess is that you could link it in some unknown,( to me), it to the instrinic magnetic moment of elementary particles but not as directly as the potentials you mention above – user108787 Nov 8 '16 at 22:20
• What do you mean by "is there a potential associated to spin"? What has being a fundamental property to do with potentials? – ACuriousMind Nov 8 '16 at 22:46
• Consider the short range spin-spin interaction in the Heisenberg hamiltonian, controlling ferromagnetism. Does it qualify, or are you hung up on long range direct interaction? The effective one is long range. – Cosmas Zachos Nov 8 '16 at 23:23
• This could be a nice conceptual question if you'll take the time to add some details of your thinking about this. – Alfred Centauri Nov 8 '16 at 23:26
• @ACuriousMind , I am sorry for not having clearified earlier, but by potential i essentially think that if two non interacting opposite spin particles are brought close to each other then what forces will they experience? – SagarM Nov 30 '16 at 22:43

You can relate the spin of a particle to its magnetic spin moment, using

$$\mathbf µ = \gamma \mathbf S$$

where $\gamma$ is the gyromagnetic ratio.

This magnetic moment could possess a magnetic potential energy if it were localised in an external magnetic field. It would depend upon the orientation of the magnetic moment vector with respect to that field,

$$U(\theta) = \mathbf µ· \mathbf B$$

However, this would only be valid for this particular situation (that is, the situation in which the particle is situated in an external magnetic field), then is not a property of the spin per se. There isn't, to my knowledge, any other way spin could be generally linked to a potential energy.

Perhaps you were wondering if objects with spin create some kind of field (which do have associated potential energies), the way electric charge and mass do. The answer is no, they don't, but neither do other fundamental properties of particles as, say, charm or strangeness. In general, those are unrelated concepts. To my understanding, "a fundamental property" just means "a property which can't be expressed in terms of something more elementary", although the definitions might vary.