Energy-momentum tensor of a ferromagnet

摘要: The energy-momentum tensor of a ferromagnet derived according to the standard prescription Noether's theorem has major flaw: term originating from spin Berry phase is gauge dependent. As consequence, some physical quantities computed show unphysical behavior. For example, presence spin-polarized current does not affect energy domain wall in commonly accepted gauge, which implies, incorrectly, absence adiabatic torque. In other gauges, torque shows glitches occurring when plane magnetization crosses Dirac string associated with magnetic monopole space. We derive gauge-invariant that free these artifacts but requires addition an extra spatial dimension, living on its boundary. It can be obtained most directly Wess-Zumino action for spins, relies same dimension.