FORMULATION OF THE SPINOR FIELD IN THE PRESENCE OF A MINIMAL LENGTH BASED ON THE QUESNE-TKACHUK ALGEBRA

In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen. 39, 10909, (2006)) introduced a (D + 1)-dimensional (beta,beta')-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal length. In this work, the Lagrangian formulation of the spinor field in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where beta' = 2 beta up to first order over deformation parameter beta. It is shown that the modified Dirac equation which contains higher order derivative of the wave function describes two massive particles with different masses. We show that physically acceptable mass states can only exist for beta < 1/8m(2)c(2). Applying the condition beta < 1/8m(2)c(2) to an electron, the upper bound for the isotropic minimal length becomes about 3 x 10(-13) m. This value is near to the reduced Compton wavelength of the electron ((lambda) over bar (c) = (h) over bar /m(e)c = 3.86 x 10(-13) m) and is not incompatible with the results obtained for the minimal length in previous investigations.