Fractional total-charge Eigenvalues for a fermion in a finite one-dimensional box

Roy, S. M. ; Singh, Virendra (1984) Fractional total-charge Eigenvalues for a fermion in a finite one-dimensional box Physics Letters B, 143 (1-3). pp. 179-182. ISSN 0370-2693

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/037026...

Related URL: http://dx.doi.org/10.1016/0370-2693(84)90830-X

Abstract

We show that the Jackiw-Rebbi and Goldstone-Wilczek hamiltonians describing a two-component Dirac fermion in bounded background field and confined to a finite one-dimensional box has self-adjoint extensions which are labelled by a 2×2 unitary matrix U. The fractional part of the eigenvalue of the total vacuum charge N0 is found to be given by α/π where det U=−exp(21α). The (non-periodic) boundary condition U=1 models the Jackiw-Rebbi infinite space solitonic situation leading to half-odd integral N0.

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