Magnon anomalous interactions from [formula omitted] gauge symmetry: Are magnons ‘charged’ under spin?

Abstract

The Pauli–Schrödinger non-relativistic theory of spin- 1 2 charged fermions requires invariance under the U ( 1 ) × SU ( 2 ) gauge group. The U ( 1 ) symmetry responds for the usual coupling of a charged particle to the electromagnetic gauge potentials A μ , while the spin interactions with the electromagnetic fields are obtained by changing the status of the global SU ( 2 ) rotational invariance of the Pauli–Schrödinger Lagrangian density to a local SU ( 2 ) gauge symmetry, for which the electric and magnetic fields E and B play the role of gauge potentials. Assuming that local gauge invariance under rotations can be applied to an arbitrary spin- S quantum field we extend the SU ( 2 ) gauge symmetry to the magnon field theory of Heisenberg ferromagnets. It is shown that the magnon field couples to the corresponding gauge fields, E and B , yielding ‘anomalous’ interactions of magnons with the electric component of the electromagnetic field, as in the case of charged excitations.