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Suppose I traps some free electrons using magnetic field and cool them to subzero temperature, can I get a super-electron this way? and does it violate the exclusion principle?

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  • $\begingroup$ How do you plan to reduce the Coulomb force between the electrons? If you don't reduce the interactions, you would get a strongly interacting system, which would not be described by the BEC theory. $\endgroup$ – Semoi Sep 20 '17 at 5:57
  • $\begingroup$ You can create a BEC with fermions, such as pairs of He3 atoms forming a superfluid near the absolute zero. The Pauli exclusion principle would not apply to the pairs, but is still would apply to individual fermions. For example, the superfluid would not reduce in volume beyond a certain limit dictated by the Pauli exclusion principle for the individual fermions. $\endgroup$ – safesphere Sep 20 '17 at 6:30
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No because electrons are fermions not bosons.

It is possible for fermions to form a BEC if they can pair up with spins opposed to form a bosonic particle. For example this is what happens in superconductivity and superfluid helium-3. However this requires some attractive force to bind the particles together. In superconductivity deformation of the crystal lattice provides the attractive force while in helium-3 it's the London force.

However for a gas of free electrons there would be no such attractive force to pair up the electrons, so they could not form a BEC.

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