Free Motion of a Dirac Particle with a Minimum Uncertainty in Position

Abstract

In this paper, we present a covariant, relativistic noncommutative algebra which includes two small deformation parameters. Using this algebra, we obtain a generalized uncertainty principle which predicts a minimal observable length in measure of space-time distances. Then, we introduce a new representation for coordinate and momentum operators which leads to a generalized Dirac equation. The solutions of the generalized Dirac equation for a free particle will be explicitly obtained. We also obtain the modified fermionic propagator for a free Dirac particle.

14 pages . . . accepted for publication in Reports on Mathematical Physics. arXiv admin note: text overlap with arXiv:1103.1015,arXiv:1103.3805 by different authors

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