In this paper, we analyze a deformation of the Heisenberg algebra consistent with both the generalized uncertainty principle and doubly special relativity. We observe that this algebra can give rise to fractional derivatives terms in the corresponding quantum mechanical Hamiltonian. However, a formal meaning can be given to such fractional derivative terms, using the theory of harmonic extensions of functions. Thus we obtain the expression of the propagator of path integral corresponding to this deformed Heisenberg algebra. In fact, we explicitly evaluate this expression for a free particle in one dimension and check its consistency. |
