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Understanding Fermi Contact forces

  1. Aug 6, 2015 #1


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    Normally, you think about SM forces being conveyed by gluons, weak force gauge bosons, or photons (ignore that troublesome gravity thing for the moment) between point particles.

    There is also a property of fermions (particles with total angular momentum Q=1/2, 3/2, etc.) that they can't occupy the same place at the same time, which is distinct from the property of bosons (particles with total angular momentum Q=1, 2, etc.) that allows more than one boson to be in the same place at the same time.

    I've heard of the term "Fermi contact force" and assumed that this is the physical effect arising from fermions not being in the same place which adds an additional (usually negligible) interaction to the three SM forces. I don't mean what Wikipedia defines as a Fermi contract interaction https://en.wikipedia.org/wiki/Fermi_contact_interaction which is an EM phenomena, so I may be using the wrong terminology, or there may be two phenomena with similar names.

    Is this correct, or is it the case, for example, that a Fermi contract force is simply a black box sort of like the four fermion "Fermi interactions" https://en.wikipedia.org/wiki/Fermi's_interaction that abstracted weak force interactions before we knew about gauge bosons?

    Or is it something entirely different?
  2. jcsd
  3. Aug 6, 2015 #2


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    First of all, the statistics of fermions do not allow several fermions to be in the same state. This is sometimes oversimplified as "being in the same place".

    The interactions you refer to are effective dimension six operators containing four fermion fields. They are part of effective field theories which appear as low energy realisations of renormalisable theories where some degrees of freedom are heavy and can be integrated out. Upon doing so, the four fermion operators appear in your effective Lagrangian. The classic example of this is Fermi's theory of weak interactions, where an operator including a proton, a neutron, a neutrino, and an electron field appear in a single operator. We now know that this theory is a low energy manifestation of the weak interactions, valid at energies smaller than the W mass, and obtained by integrating out the W as a heavy degree of freedom. It is no longer valid at energies comparable to the W mass or higher.
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