Dirac particle in gravitational quantum mechanics

In this Letter, we consider the effects of the Generalized (Gravitational) Uncertainty Principle (GUP) on the eigenvalues and the eigenfunctions of the Dirac equation. This form of GUP is consistent with various candidates of quantum gravity such as string theory, loop quantum gravity, doubly special relativity and black hole physics and predicts both a minimum measurable length and a maximum measurable momentum. The modified Hamiltonian contains two additional terms proportional to a((alpha) over bar . p)(2) and a(2)((alpha) over bar. p)(3) where alpha(i) are Dirac matrices and a similar to 1/M(p/)c is the GUP parameter. For the case of the Dirac free particle and the Dirac particle in a box, we solve the generalized Dirac equation and find the modified energy eigenvalues and eigenfunctions. (C) 2011 Elsevier B.V. All rights reserved.