Quantization of Point-Like Particles and Consistent Relativistic Quantum Mechanics

TL;DR

This paper develops a new canonical quantization scheme for relativistic point particles, ensuring a consistent quantum mechanics that accurately reflects one-particle quantum field behavior, including positive energy spectra and norms.

Contribution

It introduces a novel realization of the Hilbert space enabling consistent relativistic quantum mechanics for particles in arbitrary backgrounds.

Findings

Reproduces the positive energy spectrum of particles and antiparticles.

Ensures all state vectors have positive norms.

Provides a unified framework for quantizing relativistic particles.

Abstract

We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of the Hilbert space. It allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization a consistent relativistic quantum mechanics, which reproduces literally the behavior of the one-particle sector of the corresponding quantum field. In particular, in a physical sector of the Hilbert space a complete positive spectrum of energies of relativistic particles and antiparticles is reproduced, and all state vectors have only positive norms.