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I Four-vector related to electric and magnetic dipole moment

  1. Jul 3, 2017 #1
    What is the four-vector related to electric and magnetic dipole moment?
     
  2. jcsd
  3. Jul 3, 2017 #2
    I have never think about that. How about electromagnetic tensor ##F^{\mu\nu}## represented by ##\mathbf{P}## and ##\mathbf{M}## instead of ##\mathbf{E}## and ##\mathbf{B}## ? I am not sure at all ##\epsilon## and ##\mu## are constant in Lorentz transformation.
    Best.
     
  4. Jul 3, 2017 #3

    Orodruin

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    It is not the field tensor ##F^{\mu\nu}##, it is a separate anti-symmetric rank 2 tensor ##M^{\mu\nu}##. It is true that it is constructed from the electric and magnetic dipole moments in the same way ##F## is constructed from the electric and magnetic fields. You can then put an interaction term proportional to ##F_{\mu\nu}M^{\mu\nu}## into the Lagrangian density, effectively describing the dipole interactions.

    Edit: So to answer the OP. There is no 4-vector describing the dipole moments. The dipole moments together form an anti-symmetric rank 2 tensor. If you only consider the ##SO(3)## subgroup of spatial rotations, the 6-dimensional anti-symmetric tensor representation splits into the two 3-dimensional vector representations.

    Edit 2: Well, actually one vector representation and one pseudo vector representation ...

    Edit 3: Well, actually, if restricted to ##SO(3)## the vector and pseudo vector representations are the same ... It makes a difference if restricted to ##O(3)##.
     
    Last edited: Jul 5, 2017
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