Non-relativistic representation of the Jackiw-Rebbi soliton


  • David Valenzuela Pontificia Universidad Catolica de Chile
  • Julio César Pérez Pedraza Universidad Michoacana de San Nicolás de Hidalgo
  • Alfredo Raya Universidad Michoacana de San Nicolás de Hidalgo



Jackiw-Rebbi model, Foldy-Wouthuysen transformation, topological insulators


We consider the Foldy-Whouthuysen (FW) transformation of the Dirac equation coupled to a background soliton field which is equivalent to a position-dependent massm(x) such that at each limit x → ±∞, the mass to the left and to the right tends to a (possibly different) constant, with a sign difference at each side. We then build-up a third order unitarily transformed Schrödinger-like Hamiltonian as a counterpart of the corresponding to the well known Jackiw-Rebbi model. By further FW-transforming the Dirac spinor, we establish the relation between the non-relativistic and relativistic wave functions up to this order of approximation for generic position dependent mass profiles. For the economic choice m(x) = m0x/|x|, we find that these spinors are the same up to an overall constant.


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How to Cite

D. Valenzuela, J. C. Pérez Pedraza, and A. . Raya, “Non-relativistic representation of the Jackiw-Rebbi soliton”, Rev. Mex. Fis. E, vol. 20, no. 2 Jul-Dec, pp. 020501 1–, Jun. 2023.