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Discrete Dirac equation on a finite half-integer latticeThe formulation of the Dirac equation on a discrete lattice with half-integer spacing and periodic boundary conditions is investigated analytically. The importance of lattice formulations for problems in field theory and quantum mechanics is explained; the concept of half-integer Fourier representation is introduced; the discrete Dirac equation for the two-dimensional case is derived; dispersion relations for the four-dimensional case are developed; and the spinor formulation for the Dirac fields on the half-integer lattice and the discrete time variable for the four-dimensional time-dependent Dirac equation are obtained. It is argued that the half-integer lattice, because it takes the Dirac Lagrangian into account, is more than a mere relabeling of the integer lattice and may have fundamental physical meaning (e.g., for the statistics of fermions). It is noted that the present formulation does not lead to species doubling, except in the continuum limit.
Document ID
19870038925
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Smalley, L. L.
(NASA Marshall Space Flight Center; Alabama, University Huntsville, United States)
Date Acquired
August 13, 2013
Publication Date
March 1, 1986
Publication Information
Publication: Nuovo Cimento A, Serie 11
Volume: 92 A
ISSN: 0369-4097
Subject Category
Numerical Analysis
Accession Number
87A26199
Distribution Limits
Public
Copyright
Other

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