Perturbation theory in covariant canonical quantization

TL;DR

This paper explores a novel perturbation approach within covariant canonical quantization, demonstrating its potential to approximate quantum spectra and extend quantization methods to complex systems like quantum gravity.

Contribution

It introduces a perturbation theory framework in covariant canonical quantization and shows preliminary success in a harmonic oscillator model, suggesting broader applicability.

Findings

Reproduces quantum spectrum in a toy model

Indicates potential for quantum gravity applications

Proposes a new approximation scheme for observables

Abstract

I investigate a new idea of perturbation theory in covariant canonical quantization. I present preliminary results for a toy model of a harmonic oscillator with a quartic perturbation, and show that this method reproduces the quantized spectrum of standard quantum theory. This result indicates that when the exact solutions to classical equations are not known, covariant canonical quantization via perturbation theory could be a viable approximation scheme for finding observables, and suggests a physically interesting way of extending the scope of covariant canonical quantization in quantum gravity