It is shown that the introduction of an upper limit to the proper acceleration of a particle can smooth the problem of ultraviolet divergences in local quantum field theory. For this aim, the classical model of a relativistic particle with maximal proper acceleration is quantized canonically by making use of the generalized Hamiltonian formalism developed by Dirac. The equations for the wave function are treated as the dynamical equations for the corresponding quantum field. One may hope that using the Green’s function connected to these wave equations as propagators will improve the convergence properties of Feynman integrals.

• Received 15 December 1998

DOI:https://doi.org/10.1103/PhysRevD.60.065001