Appendix B: Breaking of the Galilei Group and Plasmon Energy Spectrum
243
and since − ˜
J i is symmetric and positive, one gets
˜
J i (ω) =
1
2 ρ B (δ(ω − ω p ) + δ(ω + ω p )),
(B.15)
i.e. a non-perturbative proof that the plasmons are the generalized quasi-particle
Goldstone excitations for the breaking of the Galilei group, with energy gap given
by the plasma frequency ω p .
243
and since − ˜
J i is symmetric and positive, one gets
˜
J i (ω) =
1
2 ρ B (δ(ω − ω p ) + δ(ω + ω p )),
(B.15)
i.e. a non-perturbative proof that the plasmons are the generalized quasi-particle
Goldstone excitations for the breaking of the Galilei group, with energy gap given
by the plasma frequency ω p .