Regularization just by quantization -- a new approach to the old problem of infinities in quantum field theory (Draft of lecture notes)

TL;DR

This paper introduces a novel regularization method for quantum field theory based on quantization by discretization, aiming to address infinities through a new representation of harmonic oscillators and Dirac delta functions.

Contribution

It proposes a new regularization approach using quantization techniques, providing a different perspective on handling infinities in quantum field theory.

Findings

Applied to scalar-field models demonstrating physical motivations.

Preliminary results on field interactions and vacuum diagrams.

Initial applications to Casimir pressure and pointlike charges.

Abstract

This is the current form of lecture notes on my approach to field quantization. I explain on a simple scalar-field model the physical motivation and show some preliminary applications (field produced by a pointlike charge, the vacuum-to-vacuum loop diagram, the Casimir presure). The approach is based on an appropriate construction of a representation of harmonic-oscillator Lie algebra and a sequential definition of Dirac deltas.