Solving the Insoluble: A New Rule for Quantization

TL;DR

This paper introduces Enhanced Quantization, a new approach that overcomes limitations of canonical quantization, successfully quantizing systems where traditional methods fail, such as rotationally symmetric and ultralocal scalar models.

Contribution

It proposes Enhanced Quantization as an alternative to canonical quantization, demonstrating its effectiveness on models where canonical methods lead to trivial or incorrect results.

Findings

Enhanced Quantization succeeds where canonical quantization fails.

Successfully quantizes rotationally symmetric and ultralocal scalar models.

Provides a new framework for consistent quantization of complex systems.

Abstract

The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced Quantization, relates classical models with their quantum partners differently and leads to satisfactory results for all systems. This paper features enhanced quantization procedures and provides highlights of two examples, a rotationally symmetric model and an ultralocal scalar model, for which canonical quantization fails while enhanced quantization succeeds.