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

  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},
  • 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… 
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