# Enhanced Quantization: The Right way to Quantize Everything

## TL;DR

Enhanced Quantization offers a novel approach that overcomes limitations of canonical quantization, enabling consistent quantization of complex fields across various spacetime dimensions without relying on Cartesian coordinates.

## Contribution

The paper introduces Enhanced Quantization, a new method that generalizes traditional procedures, allowing for non-trivial quantization of scalar fields in higher dimensions without coordinate restrictions.

## Key findings

- Overcomes triviality issues in higher-dimensional scalar fields
- Allows all classical contact transformations without operator changes
- Provides a broader framework for consistent quantization

## Abstract

Canonical quantization relies on Cartesian, canonical, phase-space coordinates to promote to Hermitian operators, which also become the principal ingredients in the quantum Hamiltonian. While generally appropriate, this procedure can also fail, e.g., for covariant, quartic, scalar fields in five-and-more spacetime dimensions (and possibly four spacetime dimensions as well), which become trivial; such failures are normally blamed on the `problem' rather than on the 'quantization procedure'. In Enhanced Quantization the association of $c$-numbers to $q$-numbers is chosen very differently such that: (i) there is no need to seek classical, Cartesian, phase-space coordinates; (ii) every classical, contact transformation is applicable and no change of the quantum operators arises; (iii) a new understanding of the importance of 'Cartesian coordinates' is established; and (iv) although discussed elsewhere in detail, the procedures of enhanced quantization offer fully acceptable solutions yielding non-trivial results for quartic scalar fields in four-and-more spacetime dimensions. In early sections, this paper offers a wide-audience approach to the basic principles of Enhanced Quantization using simple examples; later, several significant examples are cited for a deeper understanding. An historical note concludes the paper.