Quantum Electrodynamics and Planck-Scale

TL;DR

This paper explores the implications of a maximum particle momentum at the Planck scale in quantum electrodynamics, showing that divergences in the Hamiltonian become finite at this limit through Fourier analysis.

Contribution

It introduces a framework for incorporating a Planck-scale momentum cutoff in quantum electrodynamics, leading to finite self-energies and zero-point energies.

Findings

Divergent terms become finite at the Planck momentum limit.

Hamiltonian and field operator rules are explicitly derived.

Comparison of self-energies and zero-point energies at the cutoff.

Abstract

This article examines the consequences of the existence of an upper particle momentum limit in quantum electrodynamics, where this momentum limit is the Planck momentum. The method used is Fourier analysis as developed already by Fermi in his fundamental work on the quantum theory of radiation. After determination of the appropriate Hamiltonian, a Schr\"odinger equation and the associated commutation rules of the field operators are given. At the upper momentum limit mentioned above, the divergent terms occurring in the Hamiltonian (the self-energies of the electrons and the zero-point energy of the electromagnetic field) adopt finite values, which will be stated and compared with each other.