Spin resonance in Luttinger liquid with spin-orbit interaction

Spin-orbit interaction in quantum wires leads to a spin resonance at low temperatures, even in the absence of an external dc magnetic field. We study the effect of electron-electron interaction on the resonance. This interaction is strong in quantum wires. We show that the electron-electron interaction changes the shape of the resonance curve and produces an additional cusp at the plasmon frequency. However, except for very strong electron-electron interaction these changes are weak since this interaction by itself does not break the spin-rotation symmetry that is violated weakly by the spin-orbit interaction and external magnetic field.