• DOI:10.1063/1.1704281
• Corpus ID: 122748823

Exact Solution of a Many-Fermion System and Its Associated Boson Field

@article{Mattis1965ExactSO,
  title={Exact Solution of a Many-Fermion System and Its Associated Boson Field},
  author={Daniel Charles Mattis and Elliott H. Lieb},
  journal={Journal of Mathematical Physics},
  year={1965},
  volume={6},
  pages={304-312}
}

• D. Mattis, E. Lieb
• Published 1 February 1965
• Physics
• Journal of Mathematical Physics

Luttinger’s exactly soluble model of a one-dimensional many-fermion system is discussed. We show that he did not solve his model properly because of the paradoxical fact that the density operator commutators [p(p), p(−p′)], which always vanish for any finite number of particles, no longer vanish in the field-theoretic limit of a filled Dirac sea. In fact the operators p(p) define a boson field which is ipso facto associated with the Fermi-Dirac field. We then use this observation to solve the model, and obtain the exact (and now nontrivial) spectrum, free energy, and dielectric constant. This we also extend to more realistic interactions in an Appendix. We calculate the Fermi surface parameter , and find: (i.e., there exists a sharp Fermi surface) only in the case of a sufficiently weak interaction.