In 1957, Yakov Zel'dovich found that because the weak interaction violates parity symmetry, a spin- ⁠ 1 / 2 ⁠ Dirac particle must have a toroidal dipole moment, also known as an anapole moment, in addition to the usual electric and magnetic dipoles. The interaction of this term is most easily understood in the non-relativistic limit, where the Hamiltonian is H ∝ ∝ − − d ( σ σ ⋅ ⋅ E ) − − μ μ ( σ σ ⋅ ⋅ B ) − − a ( σ σ ⋅ ⋅ ∇ ∇ × × B ) , where d, μ, and a are the electric, magnetic, and anapole moments, respectively, and σ is the vector of Pauli matrices.