Phenomenological Hamiltonian in the Theory of SuperfluidHe4

Abstract

We show that a many-body Hamiltonian, expressed in terms of renormalized quasiparticle operators, has interactions only on the energy shell. Our result justifies the method of Havlin and Luban, who resolve the discrepancy between the theoretical and experimental velocity of sound in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. It also follows that the phonon spectrum must be concave at low momenta.