We propose that the phonons in ${}^4$He obey a q deformation of the Heisenberg algebra and we give an algebraic interpretation for the polynomial expansion of the small momenta phonon dispersion relation. Comparison with $C_V$ experimental data shows that our spectrum reproduces the experimental one with a less than 5% discrepancy.

• Received 22 September 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.1098