In Three Lectures On Topological Phases Of Matter section 2.1 mentioned, that: I ′ = ∫ d t d 3 x ( a → E → + b → B → ) correspond to ferromagnetism and ferroelectricity. And that I ′ ′ = ∫ d t d 3 x ( a i j E i E j + b i j B i B j ) correspondence to electric and magnetic susceptibility.Could somebody clarify, why?

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In Three Lectures On Topological Phases Of Matter section 2.1 mentioned, that:      I    ′    =  ∫  d  t      d    3    x        (                  a        →                            E        →              +                  b        →                            B        →              )  correspond to ferromagnetism and ferroelectricity. And that      I          ′      ′        =  ∫  d  t      d    3    x        (          a              i        j                    E      i              E      j        +          b              i        j                    B      i              B      j        )  correspondence to electric and magnetic susceptibility.Could somebody clarify, why?

arbotsck8sg · Accepted Answer

The energy of an electric dipole moment p/magnetic dipole moment m in the external field is proportional to it,   W  =  −      p    ⋅    E   or   W  =  −      m    ⋅    B  . In a ferromagnetic sample the local magnetic dipole moment is propotional to element of volume       d    3    x. This is just the same as you have in the expression for       I    ′  .Then, if you consider a dielectric or diamagnetic sample, it gets polarized in the external electric or magnetic field. The susceptibility is a tensor that relates, for example, the dipole moment of unit volume       P   (polarization) and the external field       E  :      P    i    =      a    j    i        E    j    .Since       P   is again the dipole moment, you get the expression       I    ″   for action

In Three Lectures On Topological Phases Of Matter section 2.1 mentioned, that: I <mi

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