Regularizing Property of the Maximal Acceleration Principle in Quantum Field Theory

TL;DR

Introducing a maximal proper acceleration in quantum field theory can mitigate ultraviolet divergences, with the model quantized via Dirac's Hamiltonian formalism leading to improved Feynman integral convergence.

Contribution

The paper demonstrates how a maximal acceleration constraint regularizes quantum field theories by quantizing a classical relativistic particle model and analyzing the resulting wave equations and propagators.

Findings

Ultraviolet divergences are smoothed by the maximal acceleration principle.

Green's functions exhibit improved convergence properties.

The approach offers a new regularization method in quantum field theory.

Abstract

It is shown that the introduction of an upper limit to the proper acceleration of a particle can smooth the problem of ultraviolet divergencies 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. Using the Green's function connected to these wave equations as propagators in the Feynman integrals leads to an essential improvement of their convergence properties.