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Fermions without fermion fields.

R C Ball1

  • 1Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom. r.c.ball@warwick.ac.uk

Physical Review Letters
|December 31, 2005
PubMed
Summary
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Researchers mapped fermion Hamiltonians to a new system without fermion fields, simplifying complex models. This finding suggests that anticommuting fermion fields may not be fundamental for observed fermion excitations.

Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Theoretical Physics

Background:

  • Fermion hopping Hamiltonians are crucial in describing many-body quantum systems.
  • Existing models, like Levin-Wen, offer simplified descriptions but have limitations.
  • The fundamental nature of anticommuting fermion fields is a long-standing question.

Purpose of the Study:

  • To generalize existing models by mapping arbitrary fermion Hamiltonians to a new representation.
  • To investigate the properties of the resulting system, particularly operator commutation relations.
  • To explore the implications for understanding fermion excitations and the necessity of anticommuting fields.

Main Methods:

  • Development of a mapping procedure for arbitrary fermion hopping Hamiltonians.

Related Experiment Videos

  • Analysis of operator commutation relations in the transformed system.
  • Application of the methods to Majorana fermions and lattice systems.

    • Main Results:

    • Successfully mapped arbitrary fermion Hamiltonians to a system devoid of fermion fields.
    • Demonstrated that operators in the new description commute, despite Fermi statistics of excitations.
    • Showed that Majorana fermions can mitigate the fermion doubling problem on Cartesian lattices.

    Conclusions:

    • The developed mapping provides a generalized and simplified framework for studying fermion systems.
    • The results challenge the necessity of anticommuting fermion fields as fundamental.
    • This work opens new avenues for theoretical investigations in quantum many-body physics.